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CIVIL  ENGINEERING  PUBLICATIONS 

NUMBER  THREE 


DESIGNING  AND  DETAILING 

OF  SIMPLE 

STEEL  STRUCTURES 


BY 


CLYDE  T.  MORRIS,  C.  E. 

PROFESSOR  OF  STRUCTURAL  ENGINEERING.  OHIO  STATE  UNIVERSITY 

MEMBER  OF  THE  AMERICAN  SOCIETY  OF  CIVIL  ENGINEERS 

MEMBER  OF  THE  SOCIETY  FOR  THE  PROMOTION 

OF  ENGINEERING  EDUCATION 


SECOND  EDITION 


COLUMBUS.  OHIO 
1910 


COPYRIGHT  1909 
COPYRIGHT  1910 

BY 
CLYDE  T.  MORRIS 


THE   HANN    *   ADAIR   PRINTING   CO..  COLUMBUS.  OHIO 


PREFACE 


The  object  sought  in  this  book  is  to  collect  from  the  many; 
larger  and  more  exhaustive  works  on  structural  steel  design, 
those  parts  which  are  applicable  to  simple  structures,  and  which 
can  be  taken  up  in  technical  schools  in  the  limited  time  usually 
allotted  to  the  subject ;  and  <at  the  same  time,  to  show  by  general 
cases  and  specific  examples  how  <the  simple  laws  of  statics  may 
be  applied  to  the  details  of  steel  structures  with  the  object  of 
producing  details  which  ,are  in  accord  with  the  stresses  they  have 
to  transmit. 

It  is  presumed  that  the  student  has  already  finished  a  course 
in  stresses,  and  little  time  is  given  here  to  the  methods  of  calcu- 
lating the  primary  stresses  in  structures. 

An  effort  has  been  made  to  make  the  nomenclature,  through- 
out, conform  to  that  used  in  "Stresses  in  Structures/'  by  Prof. 
A.  H.  Heller,  and  a  table  is  given  so  that  the  meaning  of  any 
letter  or  character  in  any  formula  can  be  at  once  determined  by 
reference  to  it.  In  some  cases  Where  reference  is  made  to  an- 
other book,  and  a  formula  is  taken  bodily  from  it,  the  nomen- 
clature of  the  original  author  is  retained  and  the  meaning  of  the 
letters  given  in  connection. 

Cross  references  to  other  articles  in  this  book  are  indicated 
by  figures  in  parentheses  giving  the  article  number,  thus  (14). 
References  to  other  works  on  the  subject  are  given  in  foot  notes. 

The  author  wishes  to  acknowledge  his  indebtedness  to  Mr. 
C.  C.  Heller  for  the  privilege  of  using  various  manuscript  notes 
and  sketches,  left  at  his  death  by  Prof.  A.  H.  Heller,  which  have 
formed  the  basis  of  many  of  the  'articles  in  this  book. 

It  is  hoped  that  by  the  illustrations  given  and  the  methods 
employed,  the  reasons  will  be  made  apparent  for  many  of  the 
details  commonly  employed  in  structural  work,  and  which  are 
many  times  put  in  by  "rule  of  thumb "  'and  too  often  without 
due  consideration  of  the  stresses  they  have  to  carry. 

In  getting  out  this  second  edition  the  author  has  corrected 
such  typographical  and  other  errors  as  have  come  to  his  notice, 
and  he  will  be  grateful  for  information  as  to  others  which  may 
be  found. 

A  little  material  has  been  tadded  to  the  chapter  on  roofs  and 
Figure  36  a  inserted,  together  with  an  estimate  of  weight. 

CLYDE  T.  MORRIS, 
Columbus,  0.,  June  23,  1910. 

222480 


TABLE  OF  CONTENTS 


PAGE 

'Chapter  I— Riveting 1 

Art.     1    Dimensions  of  Rivets 1 

Art.    2    Rivet  Holes   2 

Art.     3    Driving  Rivets  3 

Art.    4    Theory  of  Riveting 4 

Art.    5    Requirements  for  a  good  Riveted  Joint 9 

Art.     6    Proper  Sizes  of  Rivets 9 

Art.     7    Spacing  of  Rivets 10 

Art.     8    Kinds  of  Joints 12 

Art.     9    Design  of  Riveted  Connections 13 

Art.  10    Examples  of  Riveted  Joints 15 

Art.  11    Net-sections  of  Tension  Members 20 

Art.  12    Eccentric  Stresses  in  Riveted  Connections. ...  25 

Art.  13     Showing  Rivets  on  Drawings 28 

Chapter  II— Designing  and  Estimating 29 

Art.  14    Kinds  of  Structural  Steel  Work 29 

Art.  15    Kinds  of  Shops 30 

Art.  16    Proposals  and  Contracts  30 

Art.  17    Designs  and  Estimates 31 

Art.  18    Time  Savers   35 

Art.  19     Order  of  Estimating   37 

Art.  20    Specifications    41 

Art.  21    Stress  Sheets  and  General  Plans 42 

Chapter  III — Manufacture  and  Erection 44 

Art.  22     Shop  Operations  44 

Art.  23    Erection 45 

Art.  24    Drafting  Department  46 

Art.  25    A  Draftsman's  Equipment 47 

Art.  26     Ordering  Materials    51 

Art.  27    Shop  Drawings   54 

Art.  28    Order    of    Proceedure    for    a    Pin-Connected 

Bridge    62 

Art.  29    Order  of  Proceedure  for  a  Plate  Girder  Bridge  65 

IT 


TABLE  OF  CONTENTS  T 

PAGE 

Art.  30  Shop  Bills    67 

Art.  31  Shipment    69 

Art.  32  Materials   70 

Art.  33  Inspection 75 

Chapter  IV— Roofs  77 

Art.  34     Construction    77 

Art.  35    Roof  Coverings  77 

Art.  36    Types  of  Trusses 78 

Art.  37    Building  Construction 80 

Art.  38    Loads    81 

Art.  39    Stresses 84 

Art.  40    The  Design  of  a  Roof 84 

Art.  41    The  Detail  Drawings 92 

Chapter  V— Plate  Girder  Bridges  99 

Art.  42     Construction  and  Uses 99 

Art.  43     Stresses  in  Girders 99 

Art.  44    The  Web 100 

Art.  45    The  Flanges  102 

Art.  46     Economic  Depth  103 

Art.  47     Stiffeners    105 

Art.  48    Web  Splices 106 

Art.  49    Flange  Riveting   107 

Art.  50    Flange   Splices    110 

Art.  51    Design  of  a  Stringer 110 

Art.  52    Design  of  a  Deck  Plate  Girder  Bridge 115 

Art.  53     Through  Plate  Girders  137 

Chapter  VI— Pin-Connected  Bridges 139 

Art.  54    Construction   139 

Art.  55     Types  of  Trusses 139 

Art.  56    Loads    140 

Art.  5T    Tension  Members  141 

Art.  58    Compression  Members  142 

Art.  59    Lateral  Systems   146 

Art.  60  Design  of  a  Pin-Connected  Railway  Bridge. .  .146 

Art.  61    Dead  Load  147 

Art.  62    The  Depth  147 


Ti  TABLE  OF  CONTENTS 

PAGE 

Art.  63    Stresses    148 

Art.  64    Design  of  Tension  Members  150 

Art.  65    Design  of  Compression  Members  154 

Art.  66    Design  of  the  End  Posts  159 

Art.  67    The  Portal  Bracing 163 

Art.  68    Design  of  Floor  Beams 165 

Art.  69    Top  Lateral  Bracing  169 

Art.  70    Bottom  Lateral  Bracing  170 

Art.  71     Shoes  and  Boilers 171 

Art.  72    Estimate  and  Stress  Sheet 173 

Chapter  VII— Details  of  Pin-Connected  Bridges 177 

Art.  73    Pins    177 

Art.  74    Calculation  of  Pins   178 

Art.  75    Details  of  <a  Riveted  Tension  Member 182 

Art.  76  Location  of  Pins  in  Top  Chord  and  End  Post . .  185 

Art.  77    Lacing  of  Compression  Members 187 

Art.  78  Details  of  the  Floor  Beams. .                         ,  .190 


NOTATION 


!A=total  area  of  cross-section  (square  inches). 

Ap==!D.et  area  of  one  flange. 

^.w=gross  area  of  cross  section  of  web=th. 

o=distance  shown  in  the  figure. 

&=distance  shown  in  the  figure. 

0=Centrifugal  force  per  pound. 

C  <?!  <72  C"  etc.=Constants  of  integration. 

c=distance  shown  in  figure. 

Indirect  stress. 

7>.L.=dead  load  or  dead  load  stress. 

d=d'istanee  from  neutral  axis  to  a  parallel  axis. 

=depth  between  centers  of  gravity  of  the  flanges  of  -a  girder. 

=depth  between  centers  of  chords  of  a  truss. 
^=Modulus  of  elasticity. 
e=distance  shown  in  the  figure. 

=eccentricity  of  application  of  load. 
Br=horizontal  reaction. 
h=depih  of  the  web  of  a  girder,  (inches). 
7=Moment  of  Inertia, 
&=distance  Shown  in  the  figure. 

fc^distance  between  centers  of  bearings  at  the  top  of  post. 
A;2=distance  between  centers  of  bearings  at  the  bottom  of  post. 
Z^total  length. 

L.L.=live  load  or  live  load  stress. 
l^  lz  etc.=partial  lengths. 

M=moment  about  any  point  or  bending  moment. 
Ar=number  of  panels. 
P=concentrated  load  or  force. 
p=panel  length. 


=resultant  of  two  or  more  forces. 
r=radius  of  gyration. 


5=unit  stress. 

S1=miaximum  unit  stress  in  extreme  fiber. 


Ttl 


sc=unit  stress  in  compression^- 


Viii  NOTATION 

P 

— 
A. 

load  unit  stress. 
sL=]ive  load  unit  stress. 
st=unit  stress  in  tension. 
sw=working  unit  stress. 
f=thikness  of  web  of  plate  girder. 
y=vertical  reaction  due  to  horizontal  forces. 
v=distance  perpendicular  to  the  neutral  axis. 
W=total  uniform  load. 
w=load  per  foot. 
0=angle  shown  in  figure. 
=Angle  with  the  vertical  made  by  a  diagonal  truss  member. 


CHAPTER  I. 


T 


RIVETING. 

Rivets  are  used  not  only  to  connect  members  of  riveted 
structures  together,  but  also  in  all  sorts  of  steel  structures,  to 
join  parts  of  members  built  up  of  plates,  angles,  channels,  etc., 
and  for  connecting  details,  such  as  pin  plates,  lacing  bars  and 
batten  plates. 

1.  Dimensions  of  Rivets.  Rivets  are  made  in  a  machine, 
which  upsets  one  end  of  a  hot  bar  of  steel  or  iron,  forming  the 

head,  and  cuts  off  enough  of  the 
bar  to  make  a  rivet  of  the  de- 
sired length. 

The  size  of  a  rivet  is  desig- 
nated by  the  diameter  of  the 
shank,  and  its  length  under 

Lhead,  thus  %  in.  x  3^4  in. 
_i I  "Button  heads/'  which  are 

hemispherical    are    used    where 

there  is  room  for  them.  Their  size  depends  upon  the  diameter 
of  the  rivet.  Fig.  1  shows  about  the  proportions  which  are  used 
in  structural  work  for  " button  heads"  and  countersunk  rivets. 
Fig.  2  gives  the  standard  heads  used  by  The  American 
Bridge  Company.  It  will  be  noted  that  the  heads  do  not  have 
spherical  surfaces  before  driving.  The  cups  on  the  riveting 
machine  are  supposed  to  have  hollow  spherical  surfaces,  so  that 


E>uffon 


Meads 


*f\- 


American  Bridge  Company's  Standard  Rivets. 
Fig.  2. 

the  pressure  will  at  first  be  concentrated  on  the  center  of  the 
head  when  the  rivet  is  being  driven.  This  aids  in  upsetting  the 
body  of  the  rivet  so  that  it  will  fill  the  hole. 

The  grip  of  a  rivet  is  equal  to  the  sum  of  the  thicknesses 
of  the  pieces  joined.    The  distance  between  the  heads  of  a  rivet 


2  RIVET  HOLES.  Art.  2 

will  usually  exceed  the  grip,  on  account  of  the  roughness  of  the 
surfaces  of  the  parts  joined.  Allowance  is  made  for  this  in  the 
length  of  the  rivet  used,  which  must  be  long  enough  so  that 
there  will  be  sufficient  metal  to  fill  the  hole  and  form  the  head. 
A  table  of  lengths  required  for  different  grips  is  given  in  the 
hand-books  published  by  the  various  steel  companies.  (See 
Cambria,  page  337 ).1 

2.     Rivet  Holes.       Holes   for   rivets  are   either  punched, 
sub-punched  and  reamed  or  drilled.    When 
reaming   is    required,    the    amount   varies 
Punch  "|JV*/i  with  different  specifications  from  %  in.  to 

^3     i£  in>     That  is,  the  diameter  of  the 


/>X"j==U^.^          punched  is  from  %  in.  to  %  in-  smaller 
Pig  3  than    the    finished    hole.      The    object    of 

reaming  is  to  remove  the  material  sur- 
rounding the  hole  which  is  more  or  less  injured  in  punching, 
and  to  insure  a  better  -jit  and  matching  of  holes.  The  injury 
done  in  punching  is  greater  in  thick  material  than  in  thin,  and 
in  medium  steel  than  in  soft  steel.  Hard  steel  is  seldom  used 
in  structural  work. 

Where  metal  is  used  of  greater  thickness  than  the  diameter 
of  the  rivets,  it  is  usually  drilled.  Also  some  specifications  re- 
quire that  all  holes  shall  be  drilled  in  certain  cases. 

The  common  practice  is  to  use  "punched  work"  for  build- 
ings and  ordinary  highway  bridge  work,  with  both  soft  and 
medium  steel.  For  railway  bridges  the  practice  differs  very 
much  on  different  roads.  Usually  soft  steel  over  %  in.  thick, 
and  all  medium  steel  is  required  to  be  reamed.  It  is  probable 
that  the  development  of  manufacture  will  be  toward  drilling  all 
holes,  which  would  assure  a  -fit  and  matching  of  parts  which 
cannot  be  attained  with  punched  work.  Even  if  it  were  possible 
to  do  punching  accurately,  the  matching  of 
holes  would  be  difficult  to  attain  because 
punching  causes  a  piece  to  stretch,  and  the 
amount  of  stretch  depends  upon  the  thick- 
ness of  the  metal  iand  the  number  of  holes. 
For  this  reason,  as  shown  in  Fig.  4,  it  is  Fig.  4. 

necessary  to  ream  all  holes  after  the  pieces  are  assembled,  so 

*A11  references  are  made  to  the  1907  Edition. 


Art.  3.  DRIVING  RIVETS.  8 

that  the  rivets  may  be  entered.  This  is  usually  done  with  a  hand 
pneumatic  reamer.  This  reaming  does  not  produce  "reamed" 
work,  as  only  part  of  the  injured  metal  around  the  hole  is  re- 
moved. Forcing  round  tapered  pins,  called  "drift  pins,"  into 
the  holes  with  sledges,  instead  of  this  reaming,  is  not  allowable 
because  it  injures  the  metal. 

3.  Driving  Rivets.  Eivets  are  driven  hot,  and  may  be 
driven  in  three  ways ;  by  power  riveting  machines,  by  pneumatic 
hand  hammers,  or  by  hand.  Wherever  it  is  practical,  rivets  are 
driven  by  power  riveters,  because  these  produce  better  results 
at  a  less  cost. 

Power  riveting  machines  are  of  two  kinds,  direct  and  in- 
direct acting.  The  direct  acting  are  the  most  satisfactory,  as 
the  full  pressure  may  be  held  on  the  rivet  as  long  as  desired. 
In  these  machines  the  ram  moves  in  the  line  of  the  final  pressure 
throughout  the  stroke.  In  the  indirect  acting  machines,  the  cups 
are  held  in  jaws  which  are  pivoted  in  the  middle,  the  power  being 
applied  at  one  end  of  the  arm  and  the  rivet  driven  at  the  other. 
This  causes  the  cup  to  rotate  in  the  arc  of  a  circle.  Consequently 
the  cups  must  be  changed  every  time  the  grip  of  the  rivet 
changes  or  else  a  lop-sided  rivet  head  would  result. 

Machines  using  compressed  air  are  the  commonest,  and  are 
called  air  riveters.  They  are  used  as  portable  machines,  being 
hung  from  cranes  running  on  overhead  tracks  in  the  shop,  and 
do  very  good  work  if  of  proper  capacity  and  if  the  air  pressure 
is  sufficient.  A  shop  doing  girder  work  should  have  a  machine 
which  will  exert  a  pressure  of  from  50  to  60  tons.  Hydraulic 
machines  are  the  simplest  and  most  reliable,  but  they  must  be 
used  as  stationary  machines.  Steam  machines  are  also  station- 
ary, and  these  machines  >are  therefore  better  adapted  to  riveting 
light  pieces  than  large  and  heavy  ones. 

Rivets  which  must  be  driven  in  the  field  are  usually  driven 
by  hand,  but  on  large  jobs  power  is  sometimes  used.  There  are 
generally  a  few  shop  rivets  in  every  structure  which  cannot  be 
driven  by  machine  without  taking  the  piece  back,  after  an  inter- 
mediate operation,  like  planing,  has  been  performed.  Such 
rivets  are  -also  usually  driven  by  hand  or  with  pneumatic  hand 
hammers. 

The  use  of  the  pneumatic  hammer  reduces  hand  riveting  to 


4  DRIVING  EIYETS.  Art.  3 

very  small  proportions.  This  hammer  strikes  very  rapidly.  Tht3 
blows  are  comparatively  light  ones,  but  very  good  rivets  can  be 
driven  with  it.  Pneumatic  hammers  are  often  used  for  field 
riveting. 

Rivets  driven  by  power  riveters  or  pneumatic  hammers, 
through  several  thicknesses  of  plates,  which  are  then  planed 
off  to  the  center  of  the  rivet,  will  show  so  tight  that  it  is  difficult 
to  see  the  line  of  demarkation  between  the  rivet  and  the  plates. 

In  hand  riveting  the  end  of  the  shank  is  hammered  with 
hand  hammers  until  it  is  upset  roughly  into  the  form  of  a  head. 
A  "snap,"  which  is  a  hammer  with  a  cup  shaped  face,  is  then 
held  over  it  and  struck  with  a  sledge  until  the  head  is  properly 
formed  and  the  rivet  is  tight.  The  rivet  is  held  in  place  while 
being  driven  by  a  "dolly,"  which  is  a  steel  bar  with  a  cup 
shaped  face  which  fits  over  the  head  of  the  rivet. 

The  heating  of  rivets  is  important,  because  overheating,  or 
" burning'7  is  injurious,  as  well  as  doing  work  on  them  at  a 
"blue  heat."  The  range  of  temperature  at  which  wrought  iron 
may  be  worked  without  injury,  is  greater  than  for  steel,  and 
therefore  some  specifications  require  that  field  rivets  shall  be  of 
wrought  iron.  If  a  rivet  is  not  properly  heated  it  is  almost 
certain  to  be  a  bad  one.  There  are  also  times  in  a  shop,  when 
there  is  an  unusual  demand  for  power,  and  the  pressure  used 
for  driving  the  rivets  runs  too  low. 

A  loose  rivet  may  be  discovered  by  striking  the  rivet  head 
a  sharp  blow  with  a  light  hammer  specially  made  for  the  pur- 
pose. An  experienced  inspector  can  detect  loose  rivets  by  the 
jar  on  the  hand  and  the  sound  produced,  even  when  no  move- 
ment can  be  seen.  Sometimes  attempts  are  made  to  deceive 
inspectors  by  caulking  the  heads  of  loose  rivets  or  by  giving  them 
several  sharp  blows  with  the  riveting  machine. 

4.  Theory  of  Riveting.  In  spite  of  their  importance,  there 
is  no  rational  working  theory  for  designing  riveted  joints  and 
connections  under  stress.  Therefore  certain  assumptions  are 
usually  made,  which  ordinarily  render  the  design  of  riveted  con- 
nections a  very  simple  matter. 

In  a  steam  boiler  or  standpipe1  the  important  point  is  to 


1For  the   design  of   standpipes,   see  Johnson's  "Modern  Framed 
Structures,"  Chapter  XXVII. 


Art.  4.  THEORY  OF  RIVETING.  5 

get  a  maximum  efficiency  of  the  joint,  which  requires  that  we 
have  the  same  factor  of  safety  in  the  net  sections  as  in  the 
rivets.  This  subject  will  not  be  considered  here.  In  steel  build- 
ings and  bridges  it  is  simply  a  question  of  having,  at  any  point, 
a  sufficient  number  of  rivets  and  a  sufficient  net  area  to  take 
care  of  the  stress  at  the  point. 

The  following  assumptions  are  made  in  designing  riveted 
joints : 

1.  That  all  rivets  completely  fill  the  holes  into  which  they 
are  driven. 

2.  That  the  rivets  in  a  compression  member  take  the  place 
of  the  metal  punched  out,  but  that  in  a  tension  member  the 
section  is  weakened  because  the  net  section  through  the  rivet 
holes  is  less  than  the  gross  section. 

3.  That  a  rivet  cannot  safely  carry  a  tensile  stress,  that  is 
a  stress  pulling  against  its  head. 

4.  That  the  friction  between  the  parts  joined  should  be 
neglected. 

5.  That  the  bending  stress  in  the  rivets  may  be  neglected. 

6.  That  the  net  section  of  a  piece  of  steel  will  offer  the 
same  resistance  per  square  inch  as  the  gross  section. 

7.  That  the  stress  is  equally  distributed  over  the  net  sec- 
tion of  the  pieces  joined  in  tension. 

8.  That  the  stress  is  equally  distributed  over  all  the  rivets 
of  a  joint. 

These  assumptions  are  largely  interdependent  and  will  be 
considered  in  detail. 

If  a  rivet  were  perfectly  driven,  and  the  hole  completely 
filled  when  the  rivet  was  hot,  it  would  contract  in  diameter  in 
cooling.  This  contraction  precludes  an  intimate  contact  between 
the  rivet  and  the  walls  of  the  hole.* 

Regardless  of  this  fact  it  is  the  universal  practice  to  propor- 
tion compression  members  for  gross  section,  and  tension  mem- 
bers for  net  section.  An  allowance  should,  however,  be  made  in 
compression  members,  for  open  holes,  or  holes  for  loose  fitting 


According  to  experiments  by  M.  Considere  in  1886,  the  space 
between  the  rivet  and  the  side  of  the  hole,  varies  from  0.002  to  0.02 
inches.  See  Bulletin  No.  62  American  Railway  Engineering  and  Main- 
tenance of  Way  Association,  page 


6  THEORY  OF  RIVETING.  Art.  4 

bolts  or  pins.  The  allowance  to  be  made  in  tension  members 
will  be  treated  in  Art.  11. 

Coincident  with  the  contraction  in  diameter  while  cooling, 
the  length  between  heads  tends  to  decrease,  and  a  tensile  stress 
is  set  up  in  the  rivet.  In  addition  to  this  stress,  the  metal  which 
is  being  riveted  together  is  compressed  by  the  enormous  pressure 
exerted  by  the  riveting  machine,  and  when  this  pressure  is  re- 
lieved, the  metal  tends  to  resume  its  unstrained  form,  and  exerts 
a  tensile  stress  on  the  rivet.  This  initial  tension  tends  further 
to  reduce  the  diameter  of  the  cold  rivet  and  cause  a  greater 
clearance  between  the  rivet  and  the  walls  of  the  hole.  The 
amount  of  the  initial  tensile  stress  on  the  rivet  is  a  very  uncer- 
tain quantity.  It  sometimes  requires  a  very  little  pull  on  the 
head  of  a  rivet  to  break  it  off.  This  is  probably  in  part  due  to 
the  heat  treatment  which  it  has  received,  making  it  non  homo- 
geneous. Nearly  all  specifications  prohibit  the  use  of  rivets  in 
direct  tension,  but  they  are  nevertheless  so  used  in  certain  con- 
nections, because  the  construction  is  usual  and  simple.  In  these 
connections  there  are  usually  stresses  acting  at  right  angles  to 
each  other,  such  as  a  shearing  and  a  tensile  stress.  Bolts  might 
be  used  to  take  the  tension  and  rivets  to  take  the  shear,  but  rivets 
are  generally  used  throughout. 

Experiments  indicate  that  the  clearance  between  the  rivet 
and  the  walls  of  the  hole,  allows  a  slip  to  take  place  when  the 
friction  between  the  parts  is  overcome.1  Therefore  friction  is 
the  resisting  force  in  a  riveted  joint,  so  long  as  the  stress  is  not 
great  enough  to  produce  slip.  With  good  riveting  and  ordinary 
working  stresses  there  is  probably  no  slip,2  nevertheless  rivets 
are  calculated  to  resist  shearing  off.  If  a  proper  working  stress 
is  used,  the  shearing  strength  of  a  rivet  is  a  proper  measure  of 
the  friction  produced,  because  the  friction  depends  upon  the 
tension  in  the  rivet,  and  that,  as  well  as  the  shearing  strength, 
depends  upon  the  area  of  the  cross  section.  In  good  work  the 


Johnson's  "Materials  of  Construction,"  Article  375,  also 
pages  3  and  4  of  Bulletin  No.  62  American  Railway  Engineering  and  Main- 
tenance of  Way  Association. 

"Experiments  indicate  that  slip  occurs  at  a  stress  of  from  11500 
IDS.  to  21900  Ibs.  per  sq.  in.  of  rivet  cross  section. 


Art.  4.  THEORY  OF  RIVETING.  7 

slip  is  so  small  that  a  joint  may  safely  be  strained  beyond  the 
slipping  point,  if  the  stresses  do  not  alternate  in  direction? 

Practically,  it  is  considered  of  great  importance,  that  the 
rivets  should  completely  fill  the  holes  into  which  they  are  driven. 
Since  this  is  impossible  it  is  not  of  so  much  importance  so  long 
as  sufficient  friction  is  produced  between  the  parts  joined.  As 
it  requires  great  pressure  to  make  a  hot  rivet  fill  the  hole,  espec- 
ially when  the  holes  in  the  parts  joined  do  not  come  exactly 
opposite  to  each  other,  (see  Fig.  4)  this  pressure  is  useful  in 
bringing  the  parts  into  intimate  contact,  which  is  necessary  to 
develop  the  friction. 

If  no  slip  occurs,  the  only  "bending  stress  in  a  rivet  is  due  to 
elastic  deformation,  if  any  at  all  occurs.  The  longer  the  rivet 
the  less  the  bending  stress.  Usually  specifications  require  that 
the  grip  of  a  rivet  shall  not  exceed  from  four  to  five  times  its 
diameter,  on  the  supposition  that  the  rivet  transmits  the  stress. 
This  requirement  is  necessary,  because  if  the  grip  is  great  and 
the  number  of  pieces  to  be  riveted  together  is  large,  the  pressure 
exerted  by  the  riveting  machine  is  not  sufficient  to  bring  the 
pieces  into  intimate  contact  and  thus  develop  the  friction. 

When  rivet  holes  are  punched,  some  of  the  material  imme- 
diately surrounding  the  hole  is  injured,  also  a  riveting  machine 
exerts  an  enormous  pressure  on  the  metal  near  the  rivet,  and 
may  overstrain  it.  These  might  tend  to  reduce  the  permissable 
unit  stress  in  tension  on  the  net  section,2  but  experiments  show 
that  where  the  section  is  suddenly  reduced,  as  in  a  notched  bar 
or  in  a  section  through  rivet  holes,  the  ultimate  strength  per 
square  inch  is  increased  by  an  amount  which  will  more  than 
equal  the  reduction  due  to  injury.3 

If  then  the  distribution  of  stress  over  the  net  section 
through  the  rivet  holes  is  uniform,  as  per  the  7th  assumption, 
there  is  no  reason  why  the  allowable  intensity  of  stress  should 
not  be  as  great  as  for  a  section  without  rivet  holes.  If,  however, 


*See  Bulletin  No.  62  Am.  Ry.  Eng.  &  M.  of  W.  Assoc.,  pages  3  &  4. 

2See  Proceedings  of  the  Institute  of  Mechanical  Engineers,  August 
1887,  page  326. 

8See  Proceedings  of  the  Inst.  of  Mech.  Eng.,  October,  1888,  also 
eee  Heller's  "Stresses  in  Structures,"  Art.  13. 


8  THEORY  OF  RIVETING.  Art.  4 

the  stress  is  unequally  distributed,  the  maximum  intensity  will 
be  greater  than  the  7th  assumption  will  give. 

There  are  a  number  of  causes  producing  non-uniform  dis- 
tribution of  stress  over  the  net  section  through  rivet  holes.  If 
two  plates  in  tension  be  joined  by  several  rows  of  rivets,  and 
there  is  no  slip,  the  stress  is  transmitted  from  one  to  the  other 
by  means  of  the  friction  at  their  surfaces  of  contact.  This 
friction  is  greatest  under  the  rivet  heads,  because  the  friction  is 
produced  by  the  tension  in  the  rivets.  Therefore  the  intensity 
of  stress  is  greater  under  the  rivet  heads  than  half  way  between 
them.  If  the  stress  is  tensile  in  the  plates  joined,  the  uniform 
distribution  of  stress  will  be  interfered  with,  as  in  a  notched 
bar.1 

The  result  is,  no  doubt,  a  somewhat  greater  intensity  of 
stress  near  the  rivet  holes  than  half  way  between  them. 

If  the  stress  is  not  equal  on  all  the  rivets  in  a  cross  section, 
as  per  the  8th  assumption,  there  may  be  a  large  variation  in  in- 
tensity of  stress  over  the  section.  On  this  account  the  rivets  in 
a  joint  should  l>e  symmetrically  disposed  about  the  center  lines 
of  stress,  and  eccentric  stresses  avoided  wherever  possible.  If 
any  of  the  rivets  are  defective,  the  result  may  be-  the  same  as 
that  of  an  unsymmetrical  distribution. 

If  the  friction  which  is  produced  by  the  rivets  is  greatest 
Tinder  the  rivet  heads,  the  stress  is  transferred  from  one  plate 
to  the  other  in  a  series  of  increments.  The  stress  in  one  plate 
increases,  while  that  in  the  other  decreases.  The  result  is  that 
the  intensity  of  stress  in  the  two  plates  at  a  cross  section  is  not 
equal,  and  this  tends  to  cause  one  plate  to  deform  more  than 
the  other  and  thus  throw  more  stress  on  the  rivets  at  one  end  of 
the  joint  in  one  plate  and  upon  those  at  the  other  end  in  the 
other  plate.  But  the  plates  cannot  deform  unequally  as  long 
as  there  is  no  slip,  so  there  is  no  reason  why  there  should  not  be 
a  uniform  distribution  of  stress  over  the  rivets,  as  long  as  they 
are  all  in  the  same  condition.  This  would  require  perfect  work- 
manship. 


Proceedings  of  the  Inst.  of  Mech.  Eng.,  October,  1888,  also  see 
Hellers  "Stresses  in  Structures,"  Art.  13. 


Art.  5.  A  GOOD  RIVETED  JOINT.  8 

5«  Requirements  for  a  Good  Riveted  Joint.  From  the 
discussion  in  Art.  4  the  following  conclusions  may  be  drawn :  A! 
good  riveted  joint, 

1.  Should  be  as  compact  as  possible,  in  order  to  render  the 
uniform  distribution  of  stress  more  certain. 

2.  Should  not  be  very  large,  because  the  workmanship 
cannot  be  perfect,  and  there  is  the  greatest  danger  of  uneven 
distribution  of  stress  in  a  joint  having  the  largest  number  of 
rivets.    With  part  of  the  rivets  in  a  joint  defective  there  may  be 
eccentric  stresses   and  overstrain,   causing  a  redistribution  of 
stress  and  probably  overstrain  in  other  members. 

3.  Should  have  its  rivets  arranged  symmetrically  about  the 
center  lines  of  stress. 

4.  Should    have     provision    for    unavoidable     eccentric 
stresses  (see  Art.  12). 

5.  Should  have  rivets  of  good  material,  properly  driven, 
under  uniform  conditions. 

6.  Should  have  a  sufficient  number  of  rivets  so  that  there 
will  be  no  slip  if  the  stresses  alternate  in  direction. 

7.  Should  not  have  rivets  in  direct  tension. 

6.  Proper  Sizes  of  Rivets.  The  usual  sizes  of  rivets, 
which  are  seldom  departed  from  in  structural  work  are  %  in-> 
%  in.,  %  in.  and  %  in.  Rivets  larger  than  %  in.  in  diameter 
can  not  be  driven  tight  by  hand,  and  in  shops,  it  is  not  always 
possible  to  obtain  sufficient  power  to  drive  them  satisfactorily. 

It  is  a  common  rule  not  to  use  a  rivet  diameter  smaller 
than  the  thickness  of  the  thickest  plate  through  which  it  passes, 
because,  although  somewhat  thicker  plates  can  be  punched,  it  is 
often  expensive  work  on  account  of  the  breakage  of  punches. 
If  thicker  metal  is  used  it  must  be  drilled,  and  the  result  is  that 
metal  of  greater  thickness  than  about  %  in-  is  avoided. 

Tables  giving  the  maximum  size  of  rivet  which  can  be 
driven  in  various  sizes  of  structural  shapes,  and  the  location 
of  the  most  desirable  rivet  center  lines  or  "  gages, M  are  found 
in  the  handbooks  published  by  the  various  steel  companies.1 

Generally  it  is  best  to  use  the  largest  size  of  rivet  allowable 
in  each  piece,  unless  this  would  result  in  a  number  of  sizes  in 


"Cambria,"  pages  52,  53,  54  and  314. 


10 


SPACING  OF  RIVETS. 


Art.  7 


one  member,  which  would  cause  extra  handling  in  the  shop. 
Usually  but  one  or  two  different  diameters  of  rivets  are  used  in 
an  entire  structure.  When  two  different  diameters  of  rivets  are 
used  in  one  member,  the  change  should  be  made  in  such  a  manner 
that  the  two  sizes  of  holes  do  not  both  come  in  any  large  pieces, 
as  this  would  necessitate  extra  handling  in  punching.  Although 
a  %  inch  rivet  may  be  driven  in  a  3  inch  leg  of  an  angle,  a  3% 
inch  angle  should  be  used  to  make  an  important  connection  with 
%  inch  rivets. 

7.  Spacing  of  Rivets.  Rivets  are  spaced  according  to 
practical  rules  which  are  almost  universal.  It  is  evident  that 
rivet  holes  might  be  punched  so  closely  together  that  the  metal 
between  them  would  be  injured  to  such  an  extent  that  it  would 
be  of  very  little  value.  On  the  other  hand  the  rivets  might  be 
so  far  apart  that  the  parts  joined  would  not  be  in  close  contact 
between  rivets,  leaving  a  space  for  water  and  dirt  to  lodge, 
causing  rust  which  would  buckle  the  parts  and  might  develop 
high  local  stresses.  Rivets  might  also  be  spaced  so  near  the  edge 
of  a  piece  that  the  metal  would  tear  out. 

By  "pitch"  of  rivets  is  usually  meant  the  distance  center 

to  center,  parallel  to  the  line 
of  stress,  whether  the  rivets 
be  in  the  same  or  in  different 
rows.  End  distances  are  par- 
allel to  the  line  of  stress  and 
side  distances  are  perpendic- 
ular to  it.  In  Fig.  5, 
p=pitch.  e=end  distance. 
s=side  distance.  d=diameter 
of  rivet.  t=thickness  of  out- 
side plate.. 

The  following  table  gives  the  usual  specified  limits  for  rivet 
spacing,  and  Fig.  5  explains  the  terms  used. 


mm. 


_/7\ 


max.  DS  6'  or  /6t 

Fig.  5. 


Art.  7. 


SPACING  OF  RIVETS. 


11 


Diameter  of 
Rivet  in  inches 

Min.  Dist.  Cent, 
to  Cent.  Speci- 
fied in  inches 

Usual  Min.  Pitch 
for  Single  Line 
in  inches 

Maximum  Pitch 
Specified 

Usual  Maximum 
Pitch  Used 

End  Distance 
Specified  in  in. 

End  Distance 
Usually  Used 
in  inches 

.2 
8  .5 

II 

5$ 

1* 

Side  Distance 
Usually  Used 
in  inches 

d 

3d 

2d 

2d 

H 

IX 

2K 

1 

IK 

1 

lorlj 

1% 

2# 

.a 

CO 

'I 

IX 

IK 

IK 

IX 

% 

2% 

2# 

8 

g 

1% 

IK 

1% 

1# 

2% 

3 

I-H 

S 

IX 

ix 

IX 

i* 

The  minimum  pitch  in  a  double  line  may  be  less  than  in  a 
single  line,  so  long  as  the  distance  center  to  center  of  holes  in 
any  direction  is  not  less  than  the  minimum  distance  specified. 
It  is  not  the  usual  practice  to  use  the  least  allowable  pitch  unless 
there  is  a -good  reason  for  not  avoiding  it.  For  the  maximum 
pitch  16i  requires  4  in.  for  %  in-  plates  and  5  in.  for  -f$  in. 
plates.  It  is  not  good  practice  to  exceed  these  pitches,  but  in 
some  classes  of  work  6  in.  is  used  as  the  maximum  pitch  for  all 
thicknesses  of  plates.  In  the  best  classes  of  work,  no  metal  is 
used  in  important  parts,  less  than  %  in.  thick,  in  which  case 
16t=6  in. 

The  maximum  pitch  allowed  perpendicular  to  the  line  of 
stress  is  usually  about  twice  that  allowed  parallel  to  it,  but  this 
is  rarely  used  except  in  cover  plates  of  compression  members,  in 
which  case  40t  is  sometimes  allowed. 

At  the  ends  of  compression  members,  the  pitch  is  usually 
3  in.  and  should  not  exceed  four  times  the  diameter  of  the  rivet 
for  a  distance  equal  to  about  twice  the  depth  of  the  member. 
This  is  to  insure  a  uniform  distribution  of  the  stress  to  the  sev- 
eral component  parts  of  the  member. 

The  end  distance  should  never  be  less  than  1%  times  the 
diameter  of  the  rivet,  and  it  is  usually  specified  2  diameters. 
It  should  never  exceed  8  times  the  diameter  of  the  rivet. 

In  the  location  of  rivets  it  is  important  to  provide  clearance 
for  the  riveting  tool.  This  has  a  diameter  about  %  in.  greater 
than  the  diameter  of  the  head  of  the  rivet,  so  that  from  the 
center  of  the  rivet  to  the  clearance  line,  the  distance  should  be 


12 


KINDS  OF  JOINTS. 


Art.  8 


at  least  one-half  the  diameter  of  the  rivet  head  plus  %  in.  In 
special  cases  a  riveting  tool  with  one  side  cut  off,  requiring  a 
clearance  but  little  greater  than  half  the  diameter  of  the  rivet 
head,  may  be  used. 

Some  shops  have  multiple  punches,  which  punch  a  number 
of  holes  at  one  operation,  and  are  usually  used  in  connection 
with  a  spacing  table.  Certain  parts  are  punched  on  these. 
punches  and  are  not  laid  out  by  templet.  There  are  limitations 
to  the  spacing  which  the  table  can  make,  and  these  must  be 
kept  in  view  in  making  the  shop  drawings. 


Single  Riveted. 


Double  Riveted. 


-w* 


C 

>-£ 

• 

( 
C 

M 
>-< 

>j-                  1 

r 

"\     /• 

^ 

A  Jg 

0 

^Pr^p 
NTS.                          Fig.  7. 

Fig.  6. 


8.  Kinds  of  Joints.  Figures  6  to  11  show  different  kinds 
of  riveted  joints  in  plates,  and  different  arrangements  of  rivets. 
It  is  evident  that  a  lap  joint  is  much  weaker  than  a  butt  joint 
with  two  splice  plates.  In  a  lap  joint  there  is  a  moment,  having 
a  lever  arm  equal  to  the  sum  of  half  the  thicknesses  of  the  plates. 

Single  Riveted, 


Single  Riveted. 


-$!$- 

-0!$- 
"®!^" 

:  ! 

Fig.  8. 


BUTT  JOINTS. 


Fig.  9. 


//  there  were  no  deformation,  the  resulting  unit  bending  stress 
in  the  plate  would  be  six  times  the  unit  stress  due  to  direct 
stress,  but  as  the  joint  deforms  the  center  lines  of  the  plates  ap- 
proach each  other,  as  shown  in  figures  6  and  7,  and  the  moment  is 


Art.  9. 


DESIGN  OF  RIVETED  CONNECTIONS. 


13 


reduced.  The  bending  of  the  plates  will  increase  the  tensile 
stress  in  the  rivets,  and  successive  changes  of  stress,  if  great 
enough  would  loosen  them. 

Butt  joints  with  two  splice  plates  should  be  used  whenever 
possible. 

Staggered  Riveting  Chain  Riveting. 


Fig.  10. 


Fig.    11. 


9.  Design  of  Riveted  Connections.  Riveted  joints  in 
structural  steel  work  are  always  designed  upon  the  supposition 
that  the  rivets  carry  the  stress  according  to  the  assumptions 
given  at  the  beginning  of  Art.  4. 

According  to  these  assumptions  a  joint  may  fail  in  the  fol- 
lowing ways : 

1.  By  tearing  the  parts  in  tension  through  a  line  of  rivet 
holes. 

2.  By  tearing  out  the  metal  between  the  end  of  the  piece 
and  the  last  rivets. 

3.  By  shearing  the  rivets  on  one  cross  section. 

4.  By  shearing  the  rivets  on  two  cross  sections. 

5.  By  crushing  the  rivet  on  one  or  more  of  the  pieces  of 
metal  joined. 

Provision  against  tearing  through  a  line  of  rivet  holes  in 
tension  members,  will  be  treated  in  Art.  11. 

The  end  distances  usually  specified  and  which  are  given  in 
Art.  7,  provide  against  tearing  out  at  the  ends. 

If  there  is  a  tendency  to  shear  off  a  rivet  on  one  cross  sec- 
tion, it  is  said  to  be  in  single  shear^  as  in  figures  6,  7  and  8.  If 
there  is  a  tendency  to  shear  the  rivet  on  two  cross  sections,  it  is 
said  to  be  in  double  shear,  as  in  figures  9, 10  and  11. 

It  is  evident  that  if  two  plates  be  joined  together,  one  of 
them  might  be  so  thin  that  the  rivet  would  be  crushed  where  it 
bears  on  the  plate,  before  sufficient  stress  is  developed  to  shear 


14  DESIGN  OF  RIVETED  CONNECTIONS.  Art.  9 

the  rivet  off.  As  the  safety  against  crushing  depends  upon  the 
area  of  pressure  or  bearing,  and  this  depends  upon  the  thickness 
of  the  plate,  a  rivet  is  said  to  be  in  bearing  on  the  plate. 

Rivets  are  therefore  proportioned  for  single  shear,  double 
shear  or  bearing.  It  is  possible  to  have  all  of  these  to  consider 
in  a  single  joint. 

In  a  lap  joint  the  rivets  are  in  single  shear  or  bearing, 
depending  on  the  thickness  of  the  plates.  In  a  butt  joint  with 
two  splice  plates,  the  rivets  are  in  bearing  or  double  shear.  The 
bearing  may  be  either  on  the  splice  plates  or  on  the  main  plate. 
The  splice  plates  should  always  be  made  thick  enough  so  that 
the  bearing  will  be  on  the  main  plate.  That  is,  each  splice  plate 
should  be  more  than  half  as  thick  as  the  main  plate. 

There  is  no  very  definite  relation,  generally  recognized, 
between  the  working  stresses  in  tension,  shear,  and  bearing.  The 
working  stresses  for  rivets  should  depend  on  experiments.  Many 
specifications  give  a  shearing  unit  equal  to  about  three-fourths 
of  the  -tension  unit  and  a  value  in  bearing  double  that  in 
shearing.1 

The  value  of  a  rivet  in  single  shear  is  simply  the  product 
of  the  area  of  its  cross  section,  by  the  working  unit  stress  in 
shear.  Thus  the  area  of  cross  section  of  a  %  in.  rivet  is  0.44 
sq.  in.  and  its  value  in  single  shear  at  a  shearing  unit  of  7,500 
Ibs.  per  sq.  in.  is  7500X0.44=3300  Ibs.  The  value  of  a  rivet  in 
double  shear  is  twice  its  value  in  single  shear.  The  value  of  a 
rivet  in  bearing  is  taken  as  the  product  of  the  area  in  bearing 
by  the  working  unit  stress  in  bearing.  The  area  in  bearing  is 
assumed  to  be  the  diameter  of  the  rivet  multiplied  by  the  thick- 
ness of  the  piece  against  which  it  bears.  Thus  the  value  of  a 
%  in.  rivet  in  bearing  on  a  %  in.  plate  at  15,000  Ibs.  per  sq. 
in.  is  1/2 X%X  15000=6,562  Ibs.  In  designing  riveted  joints  the 
strength  of  a  rivet  is  always  figured  at  its  diameter  before  driv- 
ing. Tables  of  values  of  rivets  in  shear  and  bearing  for  several 
different  working  stresses,  are  given  in  "Cambria,"  pages 
310  and  311. 

On  account  of  the  inferiority  of  field  driven  rivets  an  excess 
of  from  25%  to  50%  over  the  requirements  for  power  driven 

*For  experiments   on  tne   ultimate   resistance   of  steel   and   iron 
plates  in  bearing  see  Johnson's  "Materials  of  Construction,"  Chapt.  XXYL 


Art.  10.  EXAMPLES  OF  RIVETED  JOINTS.  15 

rivets  is  usually  specified.     The  fractional  resistance  is  much 
less  with  hand  driven  than  with  power  driven  rivets. 

The  value  allowed  for  rivets  with  countersunk  heads  varies 
with  different  specifications.  If  the  metal,  in  which  the  counter- 
sinking is  done,  is  thick  enough  to  give  sufficient  bearing  below 
the  countersunken  part  to  develop  single  shear  in  the  rivet,  no 
reduction  need  be  made  from  the  value  used  for  rivets  with  full 
heads.  No  reduction  is  usually  made  when  the  heads  are  only 
flattened.  Rivet  heads  %  inch  or  less  high  are  countersunk. 

10.  Examples  of  Riveted  Joints.  A  few  examples  of  the 
usual  forms  of  riveted  joints  will  now  be  taken  up.  In  all  of  the 
examples  in  the  remainder  of  this  chapter  we  will  assume  the 
following  data: 

Allowed  shearing  on  rivets  7,500  Ibs.  per  sq.  in. 

Allowed  bearing  on  rivets  15,000  Ibs.  per  sq.  in. 

All  rivets  %  in-  in  diameter. 

The  values  of  rivets  in  single  shear,  double  shear,  and  bear- 
ing, may  be  taken  from  "Cambria,"  pages  310  and  311. 

Figure  6.  The  rivets  in  this  single  lap  joint  will  transmit 
3X4510=13,530  Ibs.  in  single  shear,  but  if  either  of  the  plates 
be  less  than  %  in.  thick  the  value  of  the  rivets  in  bearing  on  the 
plate  "will  be  less  than  the  single  shear  value,  and  the  amount 
of  stress  which  the  joint  will  transmit,  will  be  less  than  13,500 
Ibs.  If  the  plates  are  -^  in.  thick,  the  rivets  will  transmit 
only  3X4102=12,306  Ibs. 

The  zigzag  line  in  the  table  in  "Cambria,"  as  explained  at 
the  bottom  of  the  page,  separates  those  bearing  values  which  are 
less  from  those  which  are  greater  than  single  shear  values. 

Figure,  10.  In  this  butt  joint  with  two  splice  plates  it  is 
evident  that  the  stress  must  go  from  the  main  plate  on  one  side 
of  the  splice,  to  the  rivets  on  that  side,  from  these  to  the  splice 
plates,  from  the  splice  plates  to  the  rivets  on  the  other  side,  and 
through  them  to  the  other  main  plate. 

The  rivets  are  in  double  shear  if  the  plates  are  thick  enough. 
From  "Cambria"  we  find  that  the  value  of  a  %  in-  rivet  in 
bearing  on  a  -J-J-  in.  plate  is  equal  to  its  value  in  double  shear. 
If  therefore  the  main  plate  is  -fj  in-  thick  or  thicker,  and  the 
thickness  of  each  splice  plate  is  sufficient  to  develop  single  shear 
in  the  rivets  (%  in.  or  more),  the  rivets  of  the  joint  will  transmit 


1G 


EXAMPLES  OF  RIVETED  JOINTS. 


Art.  10 


7X9020=63,140  Ibs.  If  the  splice  plates  are  only  T^-  in.  thick, 
for  example,  the  rivets  will  transmit  only  14X4102=57,428  Ibs. 
As  stated  in  Art.  9,  the  sum  of  the  thicknesses  of  the  splice 
plates  should  always  be  greater  than  the  thickness  of  the  main 
plate. 

Figure  12  shows  the  lower  end  of  a  post  which  resists, 
through  the  pin,  the  vertical  component  of  the  stress  in  the 
diagonal  tension  member.  The  post  consists  of  two  channels 
12  in.  x  25  Ibs,  The  pin  bears  against  the  post  in  an  upward 
direction,  and  it  is  necessary  to  reinforce  the  webs  of  the  chan- 


Fig.  12. 

nels  in  order  that  the  pin  shall  not  crush  them.  Pins  are  figured 
in  shearing,  and  bearing,  exactly  similar  to  rivets,  and  usually 
the  same  unit  stresses  are  used.  Pins  must  also  be  figured  in 
bending,  and  this  will  be  treated  in  Chapter  VII. 

Assuming  the  total  stress  on  the  post  to  be  175,000  Ibs., 
the  stress  in  each  channel  will  be  87,500  Ibs.  The  thickness  of 
bearing  on  the  pin,  required  to  take  this  stress  will  be 

87500 
— —  =1.30  in.    The  total  thickness  of  pin  plates  required 

4/£   X  15000 

is  1.30  in.  minus  the  thickness  of  the  channel  web,  which  is 
0.39  in.  (See  "Cambria,"  p.  164.)  The  pin  plates  must  then  be 


Art.  10.  EXAMPLES  OF  RIVETED  JOINTS.  17 

1.30—0.39=0.91  in.  thick  or  say  f|  in.,  and  may  be  made  up  of 
one  i\  in.  and  one  %  in.  plate  as  shown. 

Enough  rivets  must  be  put  through  the  pin  plates  to  carry 
the  stresses  which  they  get  from  the  pin  to  the  web  of  the  chan- 
nel. The  total  stress  87,500  Ibs.  from  the  pin,  is  distributed  over 
f-J-  inches  thickness  of  bearing  as  follows : 

%  in.  channel  web  carries  •&  X 87500=25, 000  Ibs. 
%  in.  pin  plate  carries  -^X  87500=25,000  Ibs. 
•&•  in.  pin  plate  carries  fax 87500=37,500  Ibs. 

Total=87,500  Ibs. 

There  must  be  enough  rivets  through  each  pin  plate  to 
transmit  its  proportion  of  the  stress  to  the  channel  web,  and 
there  must  be  enough  rivets  through  the  channel  web  to  transmit 
to  it  all  of  the  stress  from  both  pin  plates. 

For  that  portion  of  the  web  which  has  a  pin  plate  on  each 
side,  the  rivets  will  be  in  bearing  on  the  web,  if  the  web  is  not 
thick  enough  to  develop  double  shear  in  the  rivets,  and  each 
rivet  will  transmit  from  each  pin  plate,  one  half  the  value  of  a 
rivet  in  bearing  on  the  web.  Therefore  the  number  of  rivets 
required  through  the  thinner  pin  plate,  will  be  found  by  divid- 
ing the  stress  carried  by  this  plate,  by  one  half  the  bearing  value 
of  a  rivet  on  the  web. 

OKAAA 

— =11  rivets  required  through  the  %  in.  pin  plate. 

These  11  rivets  will  transmit  the  same  amount  of  stress  to 
the  web,  from  the  thicker  plate  on  the  other  side  of  the  web  as 
from  the  thinner  plate.  In  addition  to  these  11  rivets,  there 
will  be  required  through  the  thicker  plate  sufficient  rivets  to 
transfer  the  difference  between  the  stresses  in  the  two  pin  plates, 
to  the  web  by  single  shear  on  the  rivets. 

37500-25000=12500  Ibs.         1250°     =3     rivets     required 

4510 

through  the  A  in.  pin  plate,  in  addition  to  the  11  rivets  through 
both. 

It  is  better  to  have  tho  pin  plates  on  opposite  sides  of  the 
web  as  shown,  but  if  necessary,  both  plates  may  be  put  on  the 
same  side,  in  which  case  the  number  of  rivets  required  through 


18 


EXAMPLES  OF  RIVETED  JOINTS. 


Art.  10 


each  would  be  determined  by  single  shear,  and  these  numbers 
would  have  to  be  added  together  to  determine  the  total  number 
required  through  the  web,  as  none  of  the  rivet  values  would  be 
determined  by  bearing  on  the  web,  unless  the  web  were  not 
thick  enough  to  develop  single  shear  in  the  rivets. 

In  this  example,  the  rivets  below  the  pin  have  been  counted, 
but  it  is  evident  that  they  can  get  no  stress  except  by  tension 
in  the  pin  plates.  No  more  stress  can  be  transmitted  to  these 
rivets  than  can  be  carried  by  the  net  area  of  the  pin  plates  at 
the  sides  of  the  pin  hole. 

Also  usually,  some  of  the  rivets  at  a  joint  like  this,  have  to 
be  countersunk  on  account  of  clearances,  in  which  case  their 
values  must  be  reduced  according  to  the  specifications  used  as 
stated  in  Art.  9. 


Cover  plate   22  "*  & 


CDQ0QQQ0QQ- 


0 •  0  Q  Q  Q'Q  Q  Q  Q  -0 — © 


Fig.  13. 

Figure  13  shows  the  top  chord  of  a  bridge  at  the  hip  joint. 
The  chord  section  is  made  up  as  follows : 


Art.  10.  EXAMPLES  OF  RIVETED  JOINTS.  19 

1  cover  plate,  22  in.  X  %  in. 

2  web  plates,  20  in.  X  A-  in. 

2  top  angles,  3y2  in.   X  3y2  in.   X  %  in. 
2  bottom  angles,  4  in.  X  3%  in.  X  %  in. 

We  will  assume  a  stress  in  this  chord  section  of  420,000  Ibs., 
and  that  the  pin  is  6%  in.  in  diameter.    This  then  will  require 

a  bearing  on  the  pin  of  6a/  \/  15ooo  —4-4  inches,  or  say  2%  inches 
on  each  side.  This  bearing  thickness  may  be  made  up  as  follows : 

Web  plate  T9T  in. 

Inside  pin  plate  %  in. 

Outside  pin  plate %  in. 

Outside  pin  plate   xV  in. 


Total— 2%  in.=  ff  in. 

The  stress  will  be  distributed  over  the  plates  as  follows: 

•&•  in.  Web  plate,  fo  X  210,000=52,500  Ibs. 

%  in.  inside  pin  plate,  HX210,000=58,300  Ibs. 
%  in.  outside  pin  plate  fg-X  210,000=58,300  Ibs. 
TV  in.  outside  pin  plate  ¥V  X  210,000=40,900  Ibs. 

Total=210,000  Ibs. 

The  rivets  in  that  portion  of  the  web,  covered  by  pin  plates 
on  both  sides,  will  be  in  bearing  on  the  web.  The  web  not  being 
thick  enough  to  develop  double  shear  in  the  rivets.  The  bearing 
value  of  a  rivet  on  the  -f$  in.  web  is  7,383  Ibs.  The  number 
of  rivets  required  in  the  ^V  in.  outside  pin  plate  will  be 

— — =11  rivets.    The  number  required  in  the  %  in.  inside 

K  X  7383 

jrQo/"v/\ 

pin  plate  will  be  i/y  ?383  =16  rivets.    More  rivets  than  required 

are  used  in  each  of  these  plates,  to  insure  a  distribution  of 
stress  to  the  upper  and  lower  rivets,  and  to  give  such  an  ar- 
rangement as  will  put  the  center  of  gravity  of  all  the  rivets  as 
near  as  possible  to  the  center  line  of  stress. 

The  number  of  rivets  through  the  outside  pin  plate  between 
the  angles,  is  determined  by  the  single  shear  value  of  a  rivet  and 


20  EXAMPLES  OF  RIVETED  JOINTS.  Art.  10 

KOOAA 

is  equal  to     451Q  =13  rivets,  all  of  which  must  be  placed  beyond 

the  rivets  required  by  the  other  two  pin  plates.  As  there  is  an 
excess  of  three  rivets  in  the  two  other  pin  plates,  one  of  the 
rivets  enclosed  by  the  dotted  line  at  "a"  may  be  counted  for 
the  outside  %  in.  pin  plate. 

Strictly,  the  rivets  passing  through  the  top  and  bottom 
angles  are  in  double  shear,  instead  of  bearing,  because  the  angles 
and  web  are  both  a  part  of  the  main  chord  section,  and  are  held 
together  by  rivets  beyond  the  pin  plates.  These  together  make 
up  a  thickness  more  than  great  enough  to  develop  double  shear 
in  the  rivets.  A  filler  %  in-  thick  will  be  required  in  this  case, 
under  the  rV  in.  outside  pin  plate,  on  the  top  angle.  This 
filler,  of  course,  takes  no  stress. 

One  outside  pin  plate,  and  all  inside  pin  plates,  should  take 
rivets  through  the  angles,  in  order  that  the  stress  may  be  dis- 
tributed over  he  entire  chord  section,  and  to  the  top  plate  in 
particular. 

This  even  distribution  of  the  stress  requires  that  the  rivets 
in  the  ends  of  compression  members,  for  a  distance  equal  to 
about  twice  the  depth,  should  be  spaced  closely  together,  as 
stated  in  Art.  7. 

No  pin  plate  should  be  shorter  than  its  width,  approxi- 
mately, or  it  might  not  be  strong  enough  to  carry  the  stress  from 
the  pin  to  the  outer  rows  of  rivets.  One  of  the  pin  plates  should 
be  long  enough  to  extend  at  least  six  inches  beyond  the  end  of 
the  batten  plate. 

Here,  as  in  Fig.  12,  some  of  the  rivets  usually  have  to  be 
countersunk  and  their  values  must  be  reduced  accordingly. 

11.  Net  Sections  of  Tension  Members.  In  a  tension 
member  it  is  not  only  necessary  to  have,  in  a  connection  or  splice, 
a  sufficient  number  of  rivets,  but  there  must  also  be  a  sufficient 
net  area  in  the  parts  joined,  and  in  the  pieces  joining  them,  to 
safely  carry  the  stress.  Therefore  in  tension  members  of  a 
structure  with  riveted  connections,  there  must  be  an  excess  of 
material,  because  the  joints  at  their  ends,  and  any  splices  in 
them,  cannot  be  made  as  strong  as  the  body  of  the  member. 

Fig.  14  shows  a  simple  tension  splice,  so  made  that  the  net 
area  is  as  great  as  possible,  and  the  waste  therefore,  as  small  as 


Art.  11. 


NET  SECTIONS  OF  TENSION  MEMBERS. 


possible.    If  the  stress  to  be  transmitted  across  the  joint  is  65,000 
Ibs.,  it  will  require   6660  =10  rivets  in  bearing  on  the  y2  inch 

plate  on  each  side  of  the  splice. 

For  getting  net  areas,  the  size  of  the  rivet  hole  is  always 
taken  as  %  in.  larger  than  the  rivet,  or  1  in.  in  diameter  for  a 
%  in.  rivet.  At  the  section  AB,  the  net  width  of  the  main  plate 
is  11  in.  The  net  area  therefore  is  11X%=5.5  sq.  in.  If  the 
allowed  unit  stress  in  tension  is  12,000  Ibs.  per  sq.  in.,  this  net 
•area  will  transmit  5.5X12,000=66,000  Ibs.  Therefore  there  is 
sufficient  net  area  at  AB. 


Fig.  14. 


At  the  section  CD  the  net  area  is  10X%=r5.0  sq.  in.,  which 
at  12,000  Ibs.  per  sq.  in.  is  good  for  60,000  Ibs.  The  rivet  at  T 
has  reduced  the  stress  carried  by  the  main  y2  in.  plate  at  CD 
to  65,000—6,560=58,440  Ibs.  There  is  then  a  little  more  net 
area  on  the  line  CD  than  is  necessary  to  carry  the  stress. 

The  stress  carried  by  the  main  %  in.  plate  at  EF  is 
65,000—3X6,560=45,320  Ibs.  The  net  section  is  9XV2=4.5  sq. 
in.,  which  is  good  for  54,000  Ibs.  In  like  manner  the  stress  in 
the  main  plate  at  GH  is  65,000—6X6,560=25,640  Ibs.,  while 
the  net  section  at  GH  is  able  to  carry  8 X%X  12,000=48,000  Ibs. 

The  net  area  of  the  splice  plates  at  any  section  must  also 
be  sufficient  to  carry  the  stress  in  them,  without  exceeding  the 
allowed  tension  unit.  At  GH  the  stress  in  the  two  splice  plates 

is  65,000  Ibs.    This  will  require  a  net  area  of  -^^  =  5.42  sq.  in. 
The  net  width  of  the  plates  at  the  point  is  12—4=8  in.,  which 


22  NET  SECTIONS  OF  TENSION  MEMBERS.  Art.  11 

will  give  a  required  thickness  of  the  two  splice  plates  of  —  ^-  =.68 
in.  and  hence  each  plate  will  have  to  be  %  in.  thick. 

The  stress  carried  by  the  splice  plates  at  EF  is  65,000—  4X 


6,560=38,760  Ibs.    The  required  net  area  is  -         =3.23  sq.  in., 


o   oo 

which  will  require  a  net  width  of  =4.31  in.,  or  a  gross 


width  of  4,31+3=7.31  in.  The  width  of  the  splice  plates  may 
be  reduced  here  some,  but  not  in  this  case  to  the  limit  of  7.31  in. 
because  this  would  not  give  sufficient  edge  distance  beyond  riv- 
ets K  and  L. 

In  figuring  these  net  areas,  only  square  sections  have  been 
taken.  It  is  obvious  that  if  the  lines  of  rivets  GH  and  EF  for 
instance,  are  close  enough  together,  the  zigzag  section 
GKMPNLH  will  have  less  net  area  than  the  square  section  GH. 
Experiments  have  been  made  on  steel  plates  which  seem  to  in- 
dicate that  rupture  will  take  place  on  the  zigzag  line  unless  its 
area  exceeds  the  area  on  the  square  section  by  at  least  30%,* 
and  some  specificaions  require  net  sections  to  be  figured  on  this 
basis.  Other  experiments  seem  to  show  that  rupture  is  equally 
probable  on  square  or  zigzag  sections  if  the  net  areas  are  equal.2 
None  of  these  experiments  may  be  a  good  guide,  because  there 
is  no  doubt  an  entirely  different  distribution  of  stress  after  the 
elastic  limit  is  exceeded  than  before,  on  account  of  the  unequal 
deformation  and  distortion  produced. 

This  is  a  difficult  matter  to  investigate  theoretically,  and 
until  further  experiments  are  made,  it  is  well  to  be  liberal  in 
allowances  for  rivet  holes.  In  Fig.  14  the  distance  between  the 
rivet  lines  GH  and  EF  which  would  be  necessary  to  give  30% 
excess  to  the  zig  zag  line  GKLH  over  the  square  section  GH,  is 
nearly  3  in.,  and  if  the  transverse  spacing  were  greater,  this 
longitudinal  distance  would  also  have  to  be  larger. 

In  nearly  all  cases  in  practice,  the  least  area  is  taken, 
whether  it  be  zigzag  or  square  section,  and  no  attention  is  paid 
to  the  30%  rule,  unless  specially  required  by  the  specifications. 

Some  specifications  give  a  simple  rule  like  the  following: 

1See  articles  by  Prof.  A.  B.  W.  Kennedy  in  Trans.  Inst.  Mech.  Eng., 
1881,  1882,  1885  and  1888. 

2See  Engineering  News,  May  3.  1906,  Vol.  LV,  page  488. 


Art.  11. 


NET  SECTIONS  OF  TENSION  MEMBERS. 


23 


"The  number  of  rivet  holes  to  be  allowed  for  in  getting  net 
section  shall  be  the  greatest  number  whose  centers  are  1%  in.1 
or  less  from  any  possible  square  cross  section."  According  to 
this  rule  the  rows  of  rivets  would  have  to  be  more  than  2%  in. 
apart,  if  the  holes  in  but  one  row  were  to  be  deducted.  This  rule 
is  not  a  safe  one  to  follow  in  all  cases,  as  will  be  seen  later. 

A  common  case  is  that  of  an  angle,  which  may  be  considered 
like  a  plate  developed,  as  in  Figs.  15,  16  and  17.  The  width  of 
the  plate  will  be  equal  to  the  sum  of  the  legs  of  the  angle  less  its 
thickness.  There  are  four  cases  according  as  the  angle  has  one, 
two,  three,  or  four  lines  of  rivets. 

In  getting  the  net  area  of  an  angle  with  one  line  of  rivets, 

allowance  is  made  for  the  area  cut  out  by  one  hole;  with  two 

V  1*  4  4      /  lines  for  one  or  two 

3?         f t-TTT  holes;    with    three 

lines  for  one,  two,  or 
three  holes,  and  with 
four  lines,  for  one, 
two,  three  or  four 
holes,  depending 
upon  the  pitch. 
Fig.  15.  In  Fig.  15  the 

stagger  of  the  holes  in  the  two  legs  is  1%  in.,  and  according  to 
the  practical  rule  above,  the  net  section  is  equal  to  the  gross 
section,  less  the  area  cut  out  by  two  holes,  or  2.75— 2ycy2=1.75 
sq.  in.  It  is  evident  that  the  holes  cut  out  a  large  percentage 
of  the  material.  The  square  section  on  AE  has  an  area  of 
2.75— lxy2=2.25  sq.  in.,  while  the  zigzag  area  ABCD  is 
(3.47— 1+2 X3/4)X%=1.98  sq.  in.,  showing  a  deficiency  in 
place  of  an  excess  in  the  zigzag  area. 

By  working  the  problem  in  the  other  direction  we  can  easily 
find  the  stagger  of  holes  necessary  to  give  us  either  an  equal  area 
or  a  30%  excess  on  the  zigzag  line,  over  the  square  section.  In 
the  case  of  Fig.  15,  it  would  require  the  stagger  to  be  at  least 
4-^  in.  in  order  that  only  one  hole  need  be  deducted  according 
to  the  30%  rule.  This  would  make  the  holes  in  one  line  at  least 
8%  in.  apart. 

The  following  table  gives  the  necessary  stagger  of  rivets  in 


Various  specifications  give  the  distance  from  1%  in.  to  2^4  in. 


24 


NET  SECTIONS  OF  TENSION  MEMBERS. 


Art.  11 


several  sizes  of  angles  with  one  line  of  rivets  in  each  leg,  to  give 
an  equal  area  and  30%  excess  area  on  the  zigzag  section,  com- 
pared with  a  square  cross  section  through  one  hole.  By  this 
table  we  see  that  the  areas  given  by  the  practical  rule  are  not 
always  safe. 


SIZE  OF  ANGLES  IN  INCHES 

Gftgej? 
in  inches 

Size  of  Riret 
in  inches 

Area  through 
Ihole 

Stagger  for 
equal  area 
in  inches 

I* 

!f 

08- 
S;Sa 
8*8 

2S» 

2X2  X  K 

1U 

% 

0  75 

1.89 

0  98 

3  04 

2  1/  V  2M  X  ^  • 

IK 

0.97 

2  26 

1  26 

3  78 

3X3  X  K 

I?/ 

% 

1  73 

2  69 

2  25 

5  53 

3^  X  3K  X  K  

2 

% 

2  75 

2  83 

3.57 

5  05 

4X  4  X  %  

2M 

% 

3  25 

3  00 

4  22 

5  68 

In  Fig.  16  the 
area  on  EG  is  4.5 
— 1  X  %  —  4.0  sq. 
in.  The  area  on 
E  F  C  D  is  y2X 
(*3,81+L5+4-2) 
=3.65  sq.  in.  The 
area  on  ABFCD  is 
%  (  3.81  +  1.5  + 
3.91  +  1.5  _  3)  = 

3.86  sq.  in.  Failure 

would  doubtless  take  place  on  EFCD  or  ABCD  but  according  to 
the  30%  rule  three  holes  would  have  to  be  deducted. 

In  Fig.  17  the  area  on  AF  is  5.75— 1X%=5.25  sq.  in.  The 
area  on  ACG  is  %(4.+6.19+1.5— 2)=4.84  sq.  in.  The  area  on 
ACDE  is  % (1.5+3.9+6.19+1.5— 3)==5.04  sq.  in.  The  area  on 
ABCDE  is  %  (1.5+3.9+3.81+3.9+1.5— 4)=5.31  sq.  in.  The 
weakest  section  is  ACG  apparently,  and  failure  would  probably 
take  place  on  this  section,  even  though  the  sections  ABCDE  and 
ACDE  have  far  less  than  30%  excess  area  over  any  square 
section. 

If  the  30%  rule  were  followed  it  would  be  necessary  to  make 


Art.  11.  NET  SECTIONS  OF  TENSION  MEMBERS.  25 

allowance  for  two  holes  at  least,  in  any  angle  having  holes  in 
both  legs,  if  the  maximum  allowed  pitch  were  not  exceeded.  (7) 

In  order  to  provide  against  undiscovered  defects  in  work- 
manship and  material,  it  is  well  to  make  a  liberal  allowance  in 
calculating  net  areas,  especially  where  stresses  are  eccentric,  as 
they  usually  are  in  angles.1 

Practice  is  not  at  all  uniform  on  this  point. 


Fig.  17. 

12.  Eccentric  Stresses  in  Riveted  Connections.  Eccen- 
tric stresses  are  seldom  calculated.  They  should  always  be 
avoided  if  possible. 

It  is  evident  that  a  single  lap  joint  like  Fig.  6  is  eccentric. 
The  forces  form  a  couple  with  a  lever  arm  equal  to  half  the  sum 
of  the  thicknesses  of  the  plates  joined,  tending  to  bend  the  plates 
and  the  rivets  (Art.  8).  The  plates  are  therefore  subjected  to  a 
bending  and  a  direct  stress.  In  a  butt  joint  with  two  splice 
plates,  (Fig.  9),  there  are  no  eccentric  stresses  in  the  plates 
joined,  but  there  are  in  the  splice  plates. 

Figure  18  shows  a  common  form  of  eccentric  connection. 
The  eccentricity  might  be  avoided  by  moving  the  force  P  to  P' 
so  that  its  line  of  action  will  pass  through  the  center  of  gravity 


^ee  Engineering  News,  Vol.  LVI,  page  14  (July  5,  1906)  for  an 
account  of  experiments  'by  Prof.  Frank  P.  McKibben,  which  show  that 
the  eccentricity  of  stress  in  angles  causes  rupture  to  occur  at  about 
80%  of  the  ultimate  strength  of  test  pieces  cut  from  the  6ame  material. 


ECCENTRIC  RIVETED  CONNECTIONS. 


Art. 


of  the  group  of  resisting  rivets.  If  it  is  impossible  to  avoid  the 
eccentricity,  the  stresses  on  the  rivets  may  be  found  as  follows. 
The  force  P,  of  16,000  Ibs.,  may  be  replaced  by  an  equal 
force  P'  parallel  to  it,  and  a  couple  whose  moment  is  16000 X 
3.18=50,800  in.  Ibs.1 


Fig.  18. 

IfiOOO 

The  direct  stress  on  each  rivet  will  be — 4——  4000  Ibs. 

To  resist  rotation  about  the  center  of  gravity  of  the  group 
of  resisting  rivets,  each  rivet  acts  in  a  direction  perpendicular 
to  its  lever  arm  and  thus  takes  an  additional  stress  in  proportion 
to  its  distance  from  the  center  of  gravity  of  the  group.  If  S' 
be  the  stress  on  each  outermost  rivet,  due  to  the  moment,  the 

equation  of  moments  will  be  2X4.5S/+2Xl1/24lfS'=5()'800 
in.  Ibs.,  from  which  we  get  S'=5080  Ibs. 

The  maximum  stress  on  each  outer  rivet  will  be  the  result- 
ant of  4000  Ibs.  and  5080  Ibs.,  which  may  be  obtained  graphically 
as  shown  in  Fig.  18.  The  resultant  for  the  two  outer  rivets  will 
not  be  the  same,  because  the  stresses  due  to  the  tendency  to 
rotate  act  in  opposite  directions.  If  the  greater  of  these  result- 
ants exceeds  the  allowed  stress  on  one  rivet,  more  rivets  must  be 
used.  The  resultant  for  rivet  A  is  8,370  Ibs.,  and  is  the  greater 
as  would  naturally  be  expected.  It  is  more  than  double  the 
stress  (4000  Ibs.)  that  it  would  receive  if  there  were  no  eccen- 
tricity. 


aThis  is  an  abstract  proposition.    See  nankine's"  Applied  Mechan- 
ics," Art.  42,  also  Heller's  "Stresses  in  Structures,"  Art.  34. 


Art.  12. 


ECCENTRIC  RIVETED  CONNECTIONS. 


27 


Figure  19  shows  another  common  form  of  eccentric  connec- 

20000 

tion.  The  direct  stress  on  each  rivet  is  -^p  =2,500  Ibs.  The 
total  moment  is  20,000X7.42=148,400  in.  Ibs.  Writing  the 
equation  of  moments  we  have  4X7.5S/+4X6.17^^  S'=148,400 

in.  Ibs.  Solving,  we  get  S'=2,950  Ibs.,  which  is  the  stress  on  A, 
By  C,  or  D  due  to  the  moment.  These  stresses  act  in  the  direc- 
tions shown  in  the  figure,  which  also  shows  the  direct  stress  on 
each  rivet.  Finding  graphically,  the  resultants  of  the  two  forces 
which  act  on  each  outer  rivet  we  have  for  A  630  Ibs.,  for  B 
3600  Ibs.,  for  C  5,410  Ibs.,  for  D  4,080  Ibs.  The  stress  on  C  is 
more  than  double  what  it  would  be  if  P  were  applied  in  the 
line  of  P'. 


Fig.  19. 

It  is  seen  from  these  examples,  that  if  the  connection  is 
eccentric,  the  rivets  are  not  equally  stressed,  and  that  simply 
taking  into  account  the  direct  stress  will  often  give  results  far 
from  the  truth. 

In  laying  out  a  joint  in  which  several  members  connect, 
rivet  lines  are  often  taken  in  place  of  center  of  gravity  lines. 
This  is  permissable  only  when  the  resulting  eccentric  stresses 
come  within  proper  limits.  If  the  rivets  in  a  joint  are  not  sym- 
metrically arranged  about  the  neutral  axes  of  the  members, 


SHOWING  RIVETS  ON  DRAWINGS. 


Art.  13 


there  will  be  eccentric  stresses.  An  angle  connected  by  one  or 
both  legs  forms  an  eccentric  connection  which  cannot  be  avoided. 
(See  foot  note,  page  25.) 

13.  Showing  Rivets  on  Drawings.  In  general  only  rivet 
heads  in  plan  are  shown  on  drawings.  They  should  always  be 
drawn  to  scale.  Where  there  is  any  possibility  of  interference 
the  rivet  heads  may  be  shown  in  elevation  as  well  as  in  plan.  In 
such  cases  the  heads  are  sometimes  only  drawn  in  pencil  to  de- 
termine the  clearance. 

In  certain  locations  there  is  not  room  enough  for  a  full  head, 
therefore  rivet  heads  may  be  flattened  or  countersunk  as  shown 
in  Fig.  20.  By  this  means  heads  may  be  made  flush  with  the 
metal  through  which  they  are  driven,  or  be  made  %  in.,  14  in. 
or  %  in.  high.  The  usual  symbols  indicating  these  various  kinds 
of  heads  are  shown  in  Fig.  20,  which  also  shows  how  open  holes 
(into  which  rivets  are  to  be  driven  in  the  field)  are  indicated. 
This  is  called  the  Osborn  system  of  symbols,  and  is  practically 
universal  in  this  country  now. 

Shop  Rivets 


fVn'n 


Counter  •st/nft  and 


CounterAun/f  not 


F/atfenffc/ 


'/atffnfd 


.   G*£M*        9 

&  ill  II 


*9£ 


fAtgh 


%'*'9f> 


Countersunk  and  ^,     Countersunk  not 


Fig.  20. 

All  the  rivets  in  a  member  need  not  be  shown  on  a  drawing, 
but  all  of  the  rivets  at  the  joints  should  be  drawn  in.  The  inter- 
mediate portions  of  the  members  are  frequently  omitted  and  the 
spacing  indicated  as  so  many  spaces  at  so  much.  In  this  case  the 
spacing  so  given  should  tie  up  two  definitely  fixed  points  at  the 
ends. 


CHAPTER  II. 
DESIGNING  AND  ESTIMATING. 

14.  Classes  of  Structural  Steel  Work.  Ordinarily  the 
term  "structural  steel"  covers  only  the  rolled  steel  used  in 
structures,  and  does  not  include  any  castings  or  machinery;  but 
in  many  classes  of  work,  machinery  is  so  intimately  connected 
with  the  structure  as  to  render  the  separate  design  of  the  two 
impossible. 

The  field  of  usefulness  of  steel  in  structural  work  is  being 
constantly  extended,  and  the  problems  of  its  design  becoming 
more  complex,  especially  for  work  in  the  more  populus  districts 
of  the  country. 

The  following  is  a  list  of  the  more  important  kinds  of  struc- 
tural steel  work : 

Bridges  for  steam  and  electric  railways  and  highways, 
I-Beam  spans, 

Longitudinal  trough  floor  spans, 
Through  and  deck  plate  girder  spans, 
Combination  bridges  (wood  and  steel), 
Simple  truss  spans, 

Draw-bridges  (swing,  lift,  rolling,  bascule,  etc.), 
Viaducts  or  trestles, 
Elevated  railways, 
Arch  bridges, 
Suspension  bridges, 
Turntables  for  locomotives, 
Trainsheds, 

Steel  mill  and  factory  buildings, 
Steel  roof  trusses, 
Grandstands, 

Steel  work  for  tall  office  buildings, 
Stand  pipes  and  elevated  tanks  and  towers, 
Steel  canal  lock  gates, 
Traveling  crane  girders, 
Ore  conveyor  bridges, 
Car  unloaders, 
Bins  for  ore,  coal,  coke,  grain,  etc. 


30  KINDS  OF  SHOPS.  Art.  15 

15.  Kinds  of  Shops.     It  may  be  said  that  no  single  plant 
in  this  country  is  well  equipped  for  turning  out  all  of  the  differ- 
ent kinds  of  structures   enumerated  in  the  preceding  article. 
Some  are  confined  to  the  manufacture  of  railway  bridges,  heavy 
highway  bridges,  and  heavy  building  work,  some  to  highway 
bridges  and  light  building  work,  some  to  steel  work  for  build- 
ings, some  shops  are  not  equipped  to  make  pin  connected  work 
and  others  cannot  do  girder  work  economically.    Some  shops  are 
not  fitted  to  handle  reamed  work.  (2). 

These  facts  are  sometimes  emphasized  by  the  manufacturer 
in  order  that  he  may  be  allowed  to  make  his  own  designs,  but 
this  should  not  be  given  too  much  weight  by  the  purchaser,  as 
all  the  usual  forms  of  details  can  be  executed  in  any  shop  fitted 
for  the  particular  kind  of  work  under  consideration  and  there 
will  seldom  be  any  difference  in  price  to  the  purchaser,  unless 
the  form  of  detail  is  an  unusual  one. 

16.  Proposals  and  Contracts.     The  requirements  of  var- 
ious purchasers  in  regard  to  proposals  and  contracts  are  not  at 
all  uniform.    The  law  requires  that  public  officials  advertise  for 
proposals  on  public  work,  and  any  manufacturer  who  meets  the 
requirements  must  be  allowed  to  bid.     The  laws  differ  in  the 
various  states.    Private  corporations,  companies  and  individuals 
do  not  usually  advertise  for  bids,  but  invite  proposals  from  such 
manufacturers  as  they  desire  to  compete  for  the  work.     They 
very  seldom  require  the  deposit  of  a  certified  check  with  the  pro- 
posal to   insure  the  signing   of  a   contract   by  the  successful 
bidder,  or  the  furnishing  of  a  bond  to  insure  the  fulfillment  of 
the  contract.    The  certified  check  and  bond  are  usually  required 
on  public  work. 

If  the  purchaser  does  not  furnish  a  design  or  plans  of  the 
work,  each  manufacturer  submits  his  own  design  with  his  pro- 
posal. This  may  be  in  accordance  with  specifications  of  his  own 
or  with  some  standard  specifications.  The  letting  of  the  contract 
then  becomes  a  question  not  only  of  the  lowest  bid  but  also  of 
the  most  desirable  design.  Usually  the  manufacturer  submits 
only  a  stress  and  section  sheet,  commonly  called  a  strain  sheet, 
but  sometimes  "show"  plans,  showing  the  general  appearance 
of  the  structure  and  some  details  of  construction  are  also  sub- 
mitted with  the  strain  sheet.  Show  plans  are  frequently  nothing 


Art.  17.  DESIGNS  AND  ESTIMATES.  31 

more  than  ornamental   drawings  on  which  the  lettering  and 
shade  lines  play  an  important  part. 

Railroads  have  bridge  engineering  departments  which  pre- 
pare the  plans  for  the  bridges.  These,  together  with  standard 
specifications,  are  submitted  to  the  bidders  who  then  all  bid 
upon  the  same  thing. 

17.  Designs  and  Estimates.  When  an  improvement  is 
contemplated  the  purchaser  should  employ  some  one  who  is 
competent  to  prepare  plans  and  specifications  and  estimates  of 
cost  of  the  proposed  work.  Also,  before  making  a  proposal,  the 
manufacturer  must  make  an  estimate  of  cost,  and  if  no  plans 
are  submitted  by  the  purchaser  on  which  to  base  the  proposal, 
he  must  also  prepare  a  design  and  plans  to  accompany  his  bid. 
In  either  case  the  method  of  procedure  in  making  the  designs 
and  estimates  will  be  essentially  the  same.  In  the  case  of  the 
manufacturer  this  work  is  done  by  the  estimating  department. 

Designs  and  estimates  must  frequently  be  prepared  upon 
the  shortest  notice,  and  in  any  case  must  be  completed  before 
the  time  set  for  receiving  bids.  Certain  methods  of  doing  the 
work  of  the  estimating  deparment  are  of  the  highest  importance, 
as  they  save  time  and  reduce  the  liability  of  errors. 

Proposals  for  bridge  work  are  asked  for  either  "lump  sum" 
or  per  pound.  In  case  a  lump  sum  price  is  required  a  very  care- 
ful estimate  is  necessary.  Usually  when  a  pound  price  is  given, 
only  an  approximate  estimate  is  made  to  give  a  general  idea  of 
the  various  quantities  of  materials  involved. 

The  estimate  of  cost  includes  such  items  as  the  following: 

Material, 

Steel  from  the  mill  (various  shapes  take  different  prices), 

Eye-bars, 

Castings,  In  case  these  are  not  manufactured 

Buckle  plates,  by  the  bidder  in  question. 

Hand  railing,  etc.J 

Labor  of  manufacture, 

Shop  labor, 

Drafting, 

General  expense, 
Freight,  Haul, 


32  DESIGNS  AND  ESTIMATES.  Art.  17 

Erection  (staging  and  false  work)  Painting, 

Lumber, 

Sub-contract  work  as  paving,  masonry  work,  etc. 

Before  the  cost  estimate  can  be  made,  of  course  the  various 
quantities  of  material  required  must  be  determined. 

The  data  furnished  for  making  the  design,  are  frequently 
very  meager  but  usually  include  specifications,  profiles  and  maps 
of  the  location. 

Before  starting  on  a  design  and  estimate,  the  first  thing 
the  designer  has  to  do  is  to  familiarize  himself  with  the  require- 
ments and  conditions  to  be  met.  Of  these  requirements  the 
specification  is  often  the  only  one  of  importance,  although  in 
some  cases  other  matters  may  demand  more  study.  The  specifi- 
cation is  a  guide  giving  the  kind  of  material  to  use,  the  loads  to 
be  assumed  as  acting  on  the  structure,  the  unit  stresses  allowed, 
the  kinds  of  details  desired,  the  quality  of  the  workmanship,  etc. 
These  will  be  discussed  more  fully  in  Art.  20. 

If  the  design  is  to  go  in  competition  with  others  it  is  im- 
portant that  it  be  an  economical  one,  that  is,  the  weight  must 
generally  be  as  small  as  possible  and  still  meet  the  requirements 
of  the  specifications.  This  is  of  course  important  to  the  purchaser 
in  any  case.  Designing  of  structures  is  not  such  an  exact  science 
that  it  may  be  said  that  all  material  in  excess  of  what  is  required 
to  take  the  calculated  stresses  is  wasted,  but  the  lightest  struc- 
ture is  generally  the  cheapest  and  usually  the  price  is  the  most 
important  determining  factor  in  selecting  a  design.  Each  case 
must,  however,  be  treated  according  to  the  peculiar  conditions 
surrounding  it.  >0nly  engineers  of  experience  can  design  really 
economic  structures.  This  matter  is  an  important  one  because 
it  is  a  matter  of  producing  a  structure  to  perform  a  certain 
function  safely  and  at  a  minimum  cost. 

No  two  estimating  departments  use  exactly  the  same  meth- 
ods. The  following  will  give  the  essential  points. 

In  order  that  the  important  requirements  of  the  specifica- 
tion may  be  easily  found  they  may  be  underscored  on  the  first 
reading,  or  an  abstract  made  omitting  such  parts  as  are  common 
to  all  specifications  and  such  parts  as  do  not  affect  the  design. 
If  a  blank  form  is  used  for  this  abstract  it  will  be  better  for 
reference.  Calculations  should  be  kept  in  some  permanent  form 


Art.  17. 


DESIGNS  AND  ESTIMATES. 


33 


for  future  reference,  the  name  of  the  structure  and  the  date 
being  prominently  indicated. 


THE  OHIC 

Sheet  No  Made  by 

>  STATE  BRIDGE  COMPANY 

Span  Extreme  

SpanC 
Pant 
Depth  ( 
Length 

Sec. 

toC  

Is  at 

Estimated  \    f  Steel  _ 

Total  Steel 

OL  per  ft.  ]    1  Floor  t 
Panel  Load  per  Truss 

c  Tract 
Tota 
DL 

Steel  per  ft  
Total  Lumber  . 

Sidewalk 

;.  to  c. 

of  Dial 

Capacity  1 
Capacity  F 

Specificatl 

russes 
loor  ' 

Tg. 

... 

MIS 

(This  3jjacefer&/a<fr0/n) 

MEM 

•ft, 

A 

impie 

Total 

Stress 

Unit 

Stress 

Req. 
Aru 

MATERIAL 

Actual 
Arti 

M. 

PC*. 

ft 

Lmtth       WEIGHT 

FORM  No.  1.    The  Form  shown  in  Fig.  22  is  to  be  used  in  connection 
with  this  one. 

Fig.  21. 


Sheet  No. 
Estimate 

THE  OHIO 

Made  by 
for 

STATE   BRIDGE  COMPANY 

Date                            '                  _     - 

MEM 

DL 

Stress 

LL 
Stress 

Impact 

Total 
Strut 

Unit 
Stress 

•H«q. 
.  Area 

MATERIAL 

Actual 
Area 

No. 
Pc«. 

Wt. 
P.  Ft. 

Length 

WEIGHT 

! 

„ 

FORM  No.  2.    This  Form  is  used  in  connection  with  Form  No.  1, 

Fig.  22. 


DESIGNS  AND  ESTIMATES. 


Art.  17 


The  information  used  in  making  estimates  of  weight  and 
cost,  and  stress  and  section  sheets,  is  set  down  on  blank  forms 
called  estimate  sheets.  If  the  estimate  is  from  plans  giving 
more  or  less  detail,  a  form  like  Fig.  23,  may  be  used.  If  a  design 
is  made  in  connection  with  the  estimate,  blanks  like  Figs.  21 
and  22  are  used.  The  usual  size  of  these  is  8%xl4  inches. 


Sheet  No  
Estimate  for 

THE  < 

i 

DHIO  STATE   BRIC 

Made  bv 

IGE  CO 

Dal 

MPANY 

M  No.  3 

MEM. 

No. 

SIZE 

Length 

Wt. 
P.  Ft. 

WEIGHTS 

OTAL 

- 

:  —        — 

.      »• 

•  -== 

:.-      •-• 

~-i 

-1—  1—  L- 

•J  '•• 

-i 

«c« 

^j^ 

-**• 

*** 

«-ta 

•*• 

*• 

_• 

a* 

--*  -- 

•'•  '•  k 

FORM  No.  3. 
Fig.  23. 

On  Form  No.  1,  in  the  space  at  the  top,  should  be  shown  a 
single  line  diagram  of  the  structure,  properly  lettered.  (For 
example  see  Art.  62.)  This  form  also  has  places  for  the  prin- 
cipal data  upon  which  the  design  is  based,  stresses,  make  up  .and 
areas  of  members  and  their  estimated  weights.  This  form  is  used 
for  sheet  No.  1  of  the  estimate.  For  the  following  sheets  Form 
No.  2  is  used,  which  is  similar  to  the  lower  part  of  Form  No.  1. 

An-  estimate  should  give  within  a  few  percent,  the  actual 
quantities  of  the  various  materials,  which  will  be  required  to 
make  the  structure.  An  estimator  must,  therefore,  not  only 
know  how  to  obtain  the  weights  of  main  members,  but  he  must 
be  thoroughly  familiar  with  detailing. 

Unless  the  estimate  is  made  from  plans  giving  details,  or  is 
for  a  plate  girder  bridge,  or  some  such  simple  structure,  the 
details  are  not  all  set  down,  but  .are  lumped  as  a  percentage  of 
the  main  parts.  A  convenient  way  of  doing  this,  for  pin  con- 
nected trusses,  is  to  make  the  details  of  each  member,  a  per- 
centage of  the  rest  of  the  member,  and  for  riveted  trusses,  a 


Art.  18.  TIME  SAVERS.  35 

percentage  of  the  balance  of  the  whole  truss.  Of  course  these 
percentages  will  vary  with  the  specifications  and  form  of  truss, 
and  must  be  determined  by  making  an  estimate  of  the  details,  or 
by  taking  them  from  previous  estimates  in  which  the  details 
have  been  estimated. 

An  estimating  department  accumulates,  in  time,  many 
valuable  tables,  such  as  tables  of  standard  connections,  joists, 
rivet  and  pin  values,  portal  stresses,  properties  of  columns, 
moment  tables,  etc.,  which  save  much  time.  Much  valuable  in- 
formation is  given  in  the  handbooks  published  by  mills  rolling 
structural  steel  shapes.  Those  gotten  out  by  the  Carnegie  Steel 
Co.  and  the  Cambria  Steel  Co.  are  the  most  complete.  Since 
they  give  the  properties  of  all  rolled  shapes,  one  of  them  is  in- 
dispensable in  making  designs  and  estimates.  Combinations  of 
shapes  are  frequently  used  for  compression  members  and  girders. 
Since  it  is  necessary  to  know  the  'radius  of  gyration  or  moment 
of  inertia  of  these  and  the  location  of  the  neutral  axes,  and 
since  calculating  these  involves  considerable  labor,  there  should 
be  some  systematic  method  of  making  the  calculations  and  of 
preserving  the  results  for  future  reference.  There  are  several 
sets  of  tables  published,  giving  the  properties  of  builtup  sections, 
and  one  of  these  will  be  a  great  help  in  designing.1 

18.  Time  Savers.  Besides  the  books  and  tables  above 
referred  to  there  are  several  instruments,  the  use  of  which  will 
save  much  time  and  mental  effort  and  reduce  mistakes  to  a 
minimum. 

The  most  important  of  these  is  the  slide  rule.  It  is,  in  fact, 
indispensable  in  this  sort  of  work.  Thacher's  cylindrical  slide 
rule  or  the  Fuller  rule  are  more  accurate  than  is  necessary  for 
the  ordinary  work  of  the  estimating  department.  A  rule  which 
will  give  results  with  a  maximum  error  of  one  in  two  hundred 
is  sufficiently  accurate  for  all  ordinary  purposes.  The  Thacher 
rule  is,  o>f  course,  very  convenient  when  more  refined  work  is 
desired.  It  will  give  results  with  a  maximum  error  of  about 
one  in  ten  thousand. 

The  ordinary  ten.  inch  Manheim  rule  will  answer  very  well, 
but  one  which  will  give  the  product  of  three  numbers  at  one 
Tables,11  by  Frank  C.  Osborn. 


"Properties  of  Steel  Sections,"  by  John  C.  Sample. 


36  TIME  SAVERS.  Art.  18 

getting  is  very  convenient.  In  getting  weights,  the  number  of 
pieces,  the  weight  per  foot  and  the  length  are  multiplied  to- 
gether. There  are  several  rules  on  which  this  operation  can  be 
performed  at  one  setting.  The  "Duplex"  rule  is  one.  This  rule 
is  ten  inches  long  and  the  setting  is  made  on  one  face  and  the 
result  read  on  the  other  by  means  of  a  runner.  On  the  "Engi- 
neer's Slide  Rule"  the  entire  operation  is  performed  on  one  face 
at  one  setting.  This  rule  is  twenty-four  inches  long  and  has  no 
runner.  The  great  advantage  of  this  rule,  aside  from  its  three 
multiple  feature,  is  the  ease  with  which  it  may  be  read.  There 
are  only  a  few  more  divisions  in  the  twenty-four  inches  than 
are  given  on  the  other  rules  in  ten  inches,  and  consequently  the 
continued  use  of  the  rule  is  not  nearly  so  trying  on  the  eyes. 
The  degree  of  accuracy  is  not  much  greater  than  that  of  the  ten 
inch  rules.  The  maximum  error  of  operations  on  the  three 
multiple  face  is  about  one  in  two  hundred.  On  the  other  face 
of  the  rule  is  an  ordinary  slide  rule  with  scales  twenty-four 
inches  long,  which  gives  results  within  one  in  five  hundred  with 
the  same  ease  on  the  eyes. 

Care  should  be  ta.ken  to  select  a  rule  which  works  easily  but 
not  loosely,  and  one  in  which  the  graduations  on  the  slide  cor- 
respond with  those  on  the  rule.  The  trial  of  a  few  simple  num- 
bers will  be  a  sufficient  test  of  its  accuracy.  For  instance,  when 
the  1  and  2  are  set  opposite  the  following  multiples  should  also 
read  exactly  opposite :  2  to  4,  2.5  to  5,  3  to  6,  etc.  A  rule  with 
a  white  celluloid  face  is  preferable. 

The  scales  on  the  slide  rule  being  logarithmic,  problems 
involving  multiplication,  division,  powers  and  roots  can  be  solved 
by  its  use.  The  books  of  instruction,  which  accompany  the  rules, 
explain  their  use  fully,  but  the  method  of  operation  can  easily 
be  discovered  by  trial  with  simple  problems.  Some  definite 
method  of  operation  should  be  adopted  and  always  followed,  to 
save  time,  so  that  it  will  be  unnecessary  to  reason  out  the  process 
each  time  a  multiplication  is  performed.  Most  problems  may  be 

resolved  into  the  simple  form  of  -^—Ans.,  and  for  these  the 
following  simple  rule  is  convenient:  "Keep  the  DIVISOR  on 
the  SLIDE  and  read  the  ANSWER  on  the  OUTSIDE."  Of 
course,  any  one  of  the  three  factors  may  be  unity,  which  pro- 
vides for  simple  multiplication  and  division. 


Art.  19.  ORDER  OF  ESTIMATING.  87 

The  decimal  point  is  best  located  by  inspection  after  the 
result  has  been  set  down. 

If  many  estimates  are  made  in  one  office,  it  should  be  pro- 
vided with  some  kind  of  an  adding  machine.  There  are  several 
such  machines  manufactured  in  this  and  other  countries.  An 
elaborate  machine,  such  as  is  used  in  banks  and  clearing  houses, 
is  not  necessary.  The  "Computometer"  is  an  excellent  machine 
but  is  somewhat  expensive.  A  small  instrument  like  the  ' '  Rapid 
Computer"  is  not  so  expensive  and  will  answer  very  well. 

19.  Order  of  Estimating.  It  is,  of  course,  very  important 
that  all  multiplications  and  additions  be  correct  within  certain 
limits,  and  every  check  possible  should  be  employed.  It  is  also 
very  important  that  no  omissions  are  made.  The  best  way  to 
insure  reliable  results  and  at  the  same  time  secure  speed  in  esti- 
mating, is  to  follow  some  fixed  order  of  performing  the  work 
and  some  definite  form  of  setting  it  down. 

The  following  forms  hiave  been  used  by  the  author  and 
will  serve  as  illustrations : 


38 


ORDER  OF  ESTIMATING. 


Art.  19 


ORDER  OF  ESTIMATING  RAILWAY  BRIDGES 


Truss  Memb.-Web  Diag. 
Web  Vert. 
Bot.  Chord 
Top  Chord      


Total  Trass  Memb. 

Pins,  Pin  Nuts. 

Shoes  &  Mas.  Pis. 

Rollers  &  Frames. 

Int.  Floor  Bms. 

End  Floor  Bms. 

Int.  Stringers. 

End  Stringers. 

Stringer  Pedestals. 

Stringer  Cross  Frames. 

Stringer  Laterals. 

Bottom  Laterals. 

Top  Laterals. 

Portals— Rods— Knees. 

Top  Struts. 

Sub  Struts. 

Sway  Rods— Knees. 

Top  &  Bot.Struts-Deck  Br. 

Bot.  End  Struts. 

Longitudinal  Struts. 

Castings;  Lead. 

Bolts  &  Spikes. 

Total  Iron  &  Steel. 


Timber  ft.  B.  M. 

Furnished  by. 

Placed  by. 
Tie  Plates. 
Specifications. 
Paint— Shop,  Field. 
Material. 
Reaming. 
Inspection  by. 
Transportation. 
Haul. 
Removal. 
Erection. 

Bid  f.  o.  b.  or  Erected. 
Certified  Check. 
Bond. 
Penalty. 

Time  of  Completion. 
Bid  Due. 
Substructure. 


Art.  19. 


ORDER  OF  ESTIMATING. 


ORDER  OF  ESTIMATING  HIGHWAY  BRIDGES. 


Truss  Memb.-Web  Diag. 
Web  Vert. 
Bot.  Chord 
Top  Chord 


Total  Truss  Memb. 
Pins,  Pin  Nuts. 
Shoes  &  Mas.  Pis. 
Rollers  &  Frames. 

End  Fl.Bms.1  Hanger   Pis. 

Int.Fl.Bms.  j    Lat.Con.&c. 

Sidewalk  Brackets. 

Fl.  Bm.  Hangers. 

Bot.  Laterals  1  Connections 

Top  Laterals/ Pins  &c. 

Portals— Rods— Knees. 

Top  Struts. 

Sub  Struts. 

Sway  Rods— Knees. 

Fl.BmJCnees — LowTrusses 

Top  &  Bot.Struts-Deck  Br. 

Bot.  End  Struts. 

Longitudinal  Struts. 

Steel  Joist— I  Bins. 

Facia,  Curbs, 

St.  Ry.,  Exp.  'Joints 
Castings. 
Bolts  &  Spikes. 

Total  Iron  &  Steel. 


Lumber 


ft.  B.  M. 


Buckle  Pis. 
St.Ry.Rails-furnished  by 

Laid  by. 
Hand  Railing. 
C.  I.  Newel  Posts. 
Cresting,  Ornaments. 
Latticed  Hub  Guard. 
Wood  Fence. 

Paving-Roadways  &  S.  "Wh 
Specifications. 
Paint— Shop,  Field. 
Material. 
Reaming. 
Inspection  by. 
Freight. 
Haul. 
Removal. 
Erection. 

Bid  f.  o.  b.  or  Erected 
Certified  Check. 
Bond. 
Penalty. 
Payment. 

Time  of  Completion. 
Bid  Due. 
Substructure. 


ORDER  OF  ESTIMATING. 


Art.  19 


ORDER  OF  ESTIMATING  STEEL  BUILDINGS. 


Trusses— Main,  Vent.,  Knees. 

Lean-to. 

Special. 

Hip  &  Valley  Rafters,  etc. 
Columns —Main. 

Clearstory. 

Crane. 

Lean-to. 

End. 

Floor. 
Struts— Latticed  Eave. 

Side,  End,  Vent. 

Special. 
Ties— Bottom  Chord. 

Special. 

Ventillator  Knees. 
Roof  Purlins— Main,  Vent. 

Lean-to,   Special. 
Purlins— Side. 

End,  Gable. 
Finish  Angles— Main  Roof. 

Vent.  Roof. 

Lean-to  Roof. 

Bods— Rafter,  Main,  Vent., 
Lean-to. 

Bottom  Chord. 

Side  Sways. 

End  Sways. 

Sag  Ties. 

Anchor  Bolts— Bolts,  &c. 
Crane   Girders— Brackets. 
Floor  Girders— 'Joist. 
Floor  Plate. 

Stairs— Tracks  for  Doors,  &c. 
Total  Steel  in  Bldg.  " 


Crane  Rails-Clips  &  Fastenings 
Corrugated  Iron— Roof. 

Sides. 

Ridge  Cap— Flashing. 
Gutters— Down  spouts. 
Slate,  Felt,  Tin,  Cornice,  &c. 
Louvers. 
Wood  Purlins,  Nailing  Strips. 

Sheeting  ft.  B.  M. 

Skylights— No.  &  size— Glazing 
Windows— No.  &  size— Glazing. 
Doors. 

Door  Frames— Window  Frames 
Skylight  Frames. 
Railings. 

Circular  Ventillators. 
Brick  Walls  &  Foundations. 
Specifications. 
Materials. 

Paint— Shop,  Field. 
Freight. 
Haul. 
Removal. 
Erection. 

Bid  f.  o.  b.  or  Erected. 
Certified  Check. 
Bond. 
Penalty. 

Time  of  Completion. 
Bid  Due. 


Art.  20.  SPECIFICATIONS.  41 

20.  Specifications.  A  specification  is  a  set  of  rules  for 
the  guidance  of  the  designer,  the  draftsman,  the  rolling  mill, 
the  shop,  the  erector  and  the  inspector.  It  is  a  part  of  the 
contract1  and  all  work  is  gotten  out  in  accordance  with  some 
specification,  and  for  bridges,  generally  in  accordance  with 
some  standard  specification.  There  are  a  number  of  bridge 
specifications  which  are  published  in  pamphlet  form  for  general 
use. 

The  following  are  some  of  the  most  used  specifications  for 
steel  railway  bridges: 

"General  Specifications  for  Steel  Railroad  Bridges''  of  the 
American  Railway  Engineering  and  Maintenance  of  "Way 
Asso-ciation. 

"General  Specifications  for  Steel  Railroad  Bridges  and 
Viaducts/'  by  Theo.  Cooper. 

"General  Specifications  for  Railway  Bridges,  by  Edwin 
Thacher. 

"General  Specifications  for  Railway  Bridge  Superstruc- 
tures/' by  The  Osborn  Engineering  Company. 

"General  Specifications  governing  the  Designing  of  Steel 
Railroad  Bridges  and  Viaducts/'  by  J.  A.  L.  Waddell. 

The  general  specifications  for  highway  bridges  usually  in- 
clude specifications  for  electric  railway  bridges  because  bridges 
frequently  serve  both  purposes.  The  following  are  some  of  the 
more  important  of  these: 

"General  Specifications  for  Steel  Highway  and  Electric 
Railway  Bridges  and  Viaducts/'  by  Theo.  Cooper. 

"General  Specifications  for  Highway  Bridges/'  by  Edwin 
Thacher. 

"General  Specifications  for  Highway  Bridge  Superstruc- 
tures/' by  The  Osborn  Engineering  Company. 

"General  Specifications  governing  the  Designing  of  High- 
way Bridges  and  Viaducts/'  by  J.  A.  L.  Waddell. 

Most  railroads  have  standard  specifications  of  their  own. 
Manufacturers  also  have  specifications  which  they  use  when  no 
other  is  designated.  The  "Manufacturers'  Standard  Specifica- 


"Engineering  Contracts  and  Specifications,"  by  J.  B.  Johnson, 
for  a  complete  discussion  of  the  subject. 


42  SPECIFICATIONS.  Art  20 

tions,"  given  in  the  various  rolling  mill  hand  books,  covers  only 
the  material  as  rolled. 

Specifications  for  bridges  carrying  electric  railways, 
adopted  by  the  Massachusetts  Railroad  Commission,  have  been 
written  by  Prof.  Geo.  F.  Swain. 

The  building  codes  of  the  various  large  cities  are  supposed 
to  govern  the  design  and  erection  of  all  buildings  within  their 
•  limits,  but  many  of  these  are  antequated  and  cannot  be  applied 
to  modern  types  of  construction. 

"General  Specifications  for  Steel  Roofs  and  Buildings/'  by 
Chas.  Evan  Fowler,  refers  only  to  mill  building  construction. 

There  are  many  points  of  similarity  in  all  specifications, 
especially  with  regard  to  certain  details.  The  tendency  in  the 
future  will,  no  doubt,  be  towards  more  uniformity  in  all  re- 
quirements for  structures  of  the  same  kind.  There  is  no  more 
profitable  study  for  the  beginner,  than  the  study  of  a  number 
of  standard  specifications.1  They  give,  among  other  things,  the 
types  of  bridges  to  be  used  for  different  spans,  clearances  re- 
quired, construction  of  the  floor,  loads  to  be  used  in  calculating 
stresses  of  all  kinds,  unit  stresses  which  must  not  be  exceeded, 
details  of  construction  such  as  lacing  for  compression  members 
and  rollers  for  expansion  bearings,  kind  of  workmanship  re- 
quired, quality  of  steel  and  timber  to  be  used,  requirements  as 
to  painting,  inspection,  testing,  etc. 

21.  Stress  Sheets  and  General  Plans.  These  are  made 
on  tracing  cloth  and  of  some  standard  size.  Each  company 
usually  has  at  least  two  standard  sizes  of  drawings.  The  com- 
mon sizes  are  8y2  in.  x  14  in.,  11%  in.  x  18  in.,  and  24  in.  x 
36  in. 

The  stress  sheet  should  show,  on  a  single  line  diagram, 
stresses,  make  up  of  each  member  and  its  area,  principal  dimen- 
sions such  as  span  length,  panel  lengths,  depth  and  width,  and 
complete  general  data.  Live  and  dead  load  stresses  should  be 
given  separately  if  the  unit  stresses  are  different.  The  maxi- 
mum shear  and  maximum  moment  should  be  given  for  plate 
girders.  It  is  also  well  to  specify  the  pitch  of  rivets  in  the 

*For  a  comparison  of  the  main  features  of  a  number  of  railway 
bridge  specifications,  see  an  article  by  Prof.  A.  H.  Heller  in  "Engi- 
neering News,"  Vol.  50,  page  444. 


Art.  21.     STRESS  SHEETS  AND  GENERAL  PLANS.       43 

flanges  of  girders,  and  the  number  of  rivets  required  in  the  end 
connections  of  floor  beams  and  stringers.  (See  stress  sheets  Figs. 
35,  53  and  166.) 

Full  general  data  should  be  given  for  reference  in  examin- 
ing the  structure  after  it  has  been  in  service  for  some  time  and 
when  it  m'ay  be  overloaded.  Under  this  head  are  included  the 
specifications  governing  the  design,  the  kind  of  steel,  the  location 
of  the  structure,  the  live  and  dead  loads  assumed,  the  grade, 
the  alignment,  the  skew  (if  any),  the  construction  of  the  floor, 
the  distance  from  base  of  rail  to  bridge  seat,  etc. 

For  bridges,  the  diagrams  usually  include  an  elevation,  a 
half  or  full  view  of  the  upper  and  lower  lateral  systems,  an  end 
elevation  and  a  cross  section. 

General  plans  may  be  simply  "show"  plans  or  plans  giving 
more  or  less  detail.  The  latter  sometimes  show  practically  every- 
thing except  the  rivet  spacing  and  lengths  of  details. 


CHAPTER  III. 
MANUFACTURE  AND  ERECTION. 

22.  Shop  Operations.  Before  taking  up  the  subject  of 
shop  drawings,  we  will  consider,  briefly,  the  method  of  proeeed- 
ure  in  the  shop  work  'and  the  erection.  This  description  will  be 
general,  as  all  classes  of  work  are  not  handled  alike  and  various 
plants  differ  somewhat  in  their  equipment  and  methods. 

When  the  shop  drawings  on  a  contract  are  complete,  blue 
prints  of  them  and  the  accompanying  bills  of  material  are  sent 
to  the  various  departments  of  the  shop.  In  the  templet  shop,  a 
wooden  templet  is  made  for  each  constituent  piece  of  each  dif- 
ferent member,  excepting,  of  course,  such  parts  as  rods,  eye 
bars,  pins,  rollers,  etc.  This  templet  is  of  the  exact  length  (or 
half  length)  of  the  finished  piece,  gives  bevels  and  has  holes 
at  every  point  where  a  rivet  hole  is  to  be  located.  It  is  to  be 
clamped  to  the  metal  for  the  purpose  of  laying  out  the  work 
to  be  done  on  each  piece.  Laying  out  directly  upon  the  metal 
is  seldom  done  because  of  the  danger  of  making  errors  and  ruin- 
ing the  steel  for  the  purpose  for  which  it  was  intended. 

When  the  steel  arrives  from  the  mill  it  is  unloaded  at  one 
end  of  the  plant  and  marked  with  the  contract  number  and 
sizes  for  future  identification.  Pieces  of  the  same  size  are  piled 
together  and  separated  from  other  sizes  as  far  as  possible,  so 
that  any  material  can  be  gotten  out  easily  at  any  time  without 
handling  other  material  which  is  not  wanted.  The  unloading 
is  usually  done  with  a  crane  of  some  sort  which  deposits  the 
material  in  the  yard,  or  at  some  plants,  in  the  shop. 

When  enough  material  on  any  contract  has  been  received 
from  the  mill  and  that  contract  is  reached  on  the  shop  pro- 
gram, the  material  is  run  into  the  shop  as  it  is  needed,  and  us- 
ually continues  straight  through  to  the  opposite  end  of  the  plant 
where  the  finished  product  is  loaded. 

The  first  operation  after  the  material  is  run  into  the  shop 
is  to  straighten  it  so  that  the  templet  may  be  applied  and  that 
all  pieces  may  be  laid  out  accurately.  This  is  done  with  presses, 
rolls  and  sledges,  The  next  operation  is  laying  out,  that  is, 


Art.  23.  ERECTION.  45 

marking  the  lines  on  which  the  material  is  to  be  sheared,  and 
with  a  center  punch,  which  fits  closely  in  the  holes  in  the  temp- 
let, the  position  of  each  rivet  hole.  Some  material  is  sheared 
to  length  first  and  then  laid  out.  From  the  shears  or  laying  out 
skids,  the  material  passes  to  the  punches  where  all  holes  for 
rivets  are  punched.  Next  the  various  pieces  which  are  to  be 
riveted  together  are  assembled  -and  fitted,  putting  enough  bolts 
through  the  rivet  holes  to  hold  the  pieces  in  position  until  the 
riveting  is  completed.  These  bolts  are  taken  out  at  the  riveting 
machine  as  the  riveting  progresses.  Before  the  pieces  are  as- 
sembled, such  faces  as  will  be  inaccessible  after  riveting  are 
painted,  and  before  the  riveting  is  done  the  holes  are  reamed  out 
to  correct  inaccuracies  in  punching,  or  if  reaming  is  required 
it  is  done  at  this  time  (2).  Some  pieces  require  planing,  boring, 
chipping  and  hand  riveting  after  the  power  riveting  is  done. 

After  all  the  operations  have  been  performed  on  a  piece, 
it  is  run  on  to  a  scale  and  weighed  by  the  shipper,  who  makes 
out  a  shipping  bill.  Having  been  weighed  and  inspected  to  see 
that  it  conforms  with  the  drawing  it  is  painted  and  loaded  upon 
cars  or  stored  to  go  out  when  wanted. 

All  bending,  forge  work,  upsetting,  etc.,  are  usually  done 
in  the  blacksmith  shop.  Turning,  planing  (except  rotary  plan- 
ing) and  all  machine  work  are  done  in  the  machine  shop. 

23.  Erection.  Putting  up  the  work  in  the  field  may  be 
a  very  simple  operation  or  one  involving  the  use  of  a  large 
plant  and  considerable  risk,  depending  upon  the  character  of 
the  structure  and  its  location. 

Bridges  are  usually  erected  on  false  work,  which  consists  of 
wooden  trestles,  by  means  of  a  traveler  or  gallows  frame,  to 
which  the  tackle  for  hoisting  all  material  into  place  is  fastened. 
A  gallows  frame  consists  simply  of  two  wooden  posts  connected 
together  at  their  tops  by  a  beam  and  braces.  The  posts  usually 
rest  upon  temporary  stringers  outside  of  the  line  of  the  girders 
or  trusses.  A  traveler  has  four  legs,  at  least,  braced  together 
longitudinally  and  transversely  allowing  room  enough  under  it 
to  erect  the  bridge  inside  of  it.  It  runs  on  wheels  so  that  it  may 
be  moved  lengthwise  of  the  bridge  as  the  erection  progresses. 

Generally  during  the  erection  of  railroad  bridges  the  traffic 
must  not  be  interfered  with,  but  trains  usually  reduce  their 


46  THE  DRAFTING  DEPARTMENT.  Art.  24 

speed  and  ran  slowly  over  a  bridge  which  is  being  renewed.  The 
floor  system  is  sometimes  put  in  place  before  the  trusses  and 
blocked  up  somewhat  higher  than  its  final  position.  The  trusses 
are  erected  beginning  at  the  center,  putting  up  one  half  and 
then  moving  the  traveler  back  to  the  center  and  working  toward 
the  other  end.  Enough  bolts  are  put  into  the  connections,  which 
are  to  be  riveted,  to  fill  about  two-thirds  of  the  holes.  After 
everything  is  connected  together,  the  bridge  is  "swung,"  that  is, 
the  blocking  between  it  and  the  false  work  is  taken  out  and  it 
becomes  self-supporting.  Rivets  for  connections  of  tension 
members  of  trusses  are  driven  before  the  bridge  is  swung  and 
all  others  after  it  is  swung. 

In  the  designing  and  detailing  of  steel  structures  it  is  im- 
portant that  the  manner  of  erecting  them  be  constantly  kept  in 
mind.  Field  splices  must  be  placed  in  the  proper  positions, 
connections  should  be  designed  with  a  view  to  facility  in  mak- 
ing them  under  the  conditions  which  obtain  in  the  field;  field 
rivets  should  be  located  where  they  can  be  easily  driven;  suffi- 
cient clearance  must  be  provided  at  all  joints.  All  pieces  should 
have  plain  marks  for  identification  and  a  good  erection  diagram, 
showing  all  marks,  should  be  made.1 

24.  The  Drafting  Department.  The  organization  of  the 
drafting  department  in  various  companies  differs  greatly. 
Usually  there  is  a  chief  draftsman  who  has  general  supervision 
of  all  work  and  assigns  the  work  to  the  various  men  under  him, 
whom  he  deems  best  fitted  to  get  out  the  drawings  for  it.  Gen- 
erally a  contract  is  given  to  a  squad  foreman,  who  has  three  or 
four  men  working  under  him  and  who  directs  the  method  of 
getting  out  the  work,  writes  the  order  bills  for  the  material,  and 
sometimes  makes  some  of  the  more  complicated  drawings.  When 
the  drawings  are  made  and  traced  they  are  sent  to  a  "checker," 
who  is  generally  an  old  experienced  draftsman,  and  he  checks 
every  dimension  and  size  given  on  the  drawing  and  marks  such 
changes  as  are  necessary,  in  pencil.  The  drawing  is  then  cor- 
rected by  the  one  who  made  it,  -and  after  being  accepted  and 
signed  by  the  checker  is  ready  to  send  to  the  blueprint  room. 

*For  details  of  tools,  tackle,  traveler,  false  work,  etc.  see  Chapter 
XIII  in  Du  Bois'  "Framed  Structures,"  by  John  Sterling  Deans,  M.  Am. 
Soc.  C.  E.,  and  Appendix  C  in  Johnson's  " Modern  Framed  Structures." 


Art.  25.  A  DRAFTSMAN'S  EQUIPMENT.  47 

The  man  who  makes  the  drawing  and  the  checker  are  held 
equally  responsible  for  any  errors. 

Drawing  boards  should  be  used,  as  it  is  very  inconvenient 
to  have  to  remove  a  tracing  from  a  table  top  in  order  to  make 
a  lay  out  or  to  work  a  short  time  on  another  drawing.  The  draw- 
ing boards  should  be  of  pine  so  made  that  they  will  not  warp 
or  split.  They  should  have  one  true  edge,  preferably  of  hard 
wood,  at  the  left  hand  end. 

T-squares  should  have  rigid  heads  and  true  edges. 

The  draiving  table  should  be  large  enough  to  accommodate 
the  drawing  board,  reference  drawings,  etc.  It  should  be  at 
least  six  feet  long,  and  supplied  with  a  drawer  for  instruments, 
etc.  It  should  be,  preferably,  adjustable  as  to  height  and  slope 
of  top.  The  stool  accompanying  it  should  be  adjustable  for 
height. 

The  lighting  of  the  drawing  room  should,  of  course,  be  the 
best  possible.  If  artificial  light  is  used  at  any  time,  it  should  be 
a  diffused  light  reflected  from  the  ceiling.  A  comparatively 
quiet,  well  ventilated,  clean  and  orderly  office  will  be  conducive 
to  good  work  and  little  friction.  Unfortunately  all  of  these 
reasonable  conditions  are  not  usually  obtained. 

A  suitable  filing  system  should  be  provided  for  all  drawings 
and  other  data,  preferably  in  a  fire  proof  vault. 

25.  A  Draftsman's  Equipment.  Shop  drawings  are  the 
working  drawings  used  in  the  shop  and  give  all  details.  Making 
shop  drawings  is  the  foundation  upon  which  a  bridge  engineer's 
future  advancement  is  based.  A  draftsman  makes  his  own 
reputation.  Conditions  have  been  such  in  the  past  that  advance- 
ment comes  to  the  draftsman  about  as  rapidly  as  he  is  able  to 
take  advantage  of  his  opportunities.  One  who  makes  himself 
thoroughly  acquainted  with  the  theory  of  everything  he  does, 
one  who  is  not  afraid  of  a  little  work  outside  of  office  hours,  who 
carefully  studies  and  considers  every  piece  of  work  entrusted  to 
him,  will  not  find  the  work  growing  monotonous.  A  reputation 
for  making  mistakes  is  perhaps  the  worst  a  draftsman  can  make 
for  himself.  The  fact  that  every  drawing  is  checked  should 
have  no  influence  upon  the  amount  of  care  bestowed  on  it. 
Errors  will  sometimes  pass  the  checker  and  are  expensive  in 
nearly  all  cases.  Errors  are  especially  liable  to  occur  when 


48  A  DRAFTSMAN'S  EQUIPMENT.  Art.  25 

changes  are  made  necessary  after  a  drawing  is  made,  either 
before  or  after  it  is  checked.  For  this  reason  a  draftsman  should 
do  everything  according  to  some  method.  There  is  a  best  place 
to  begin  on  a  structure  and  a  most  logical  order  in  which  to 
work  it  up,  not  only  each  drawing  but  every  detail.  If  this  is 
followed  very  little  erasing  will  have  to  be  done,  and  everything 
will  be  better  designed  than  if  one  detail  is  worked  out  regard- 
less of  everything  else  and  afterwards  fudged  to  correspond 
with  other  requirements.  After  changes  are  made  the  drawing 
is  usually  out  of  scale,  and  not  drawing  to  scale  is  usually  con- 
ducive to  mistakes.  Even  rivet  heads  should  ~be  to  scale. 

Every  drafting  room  has  some  peculiar  practices  of  its 
own,  and  it  is  generally  the  part  of  wisdom  for  a  new-comer  to 
conform  with  them  as  soon  as  he  can  find  out  what  they  are. 

A  draftsman 's  outfit  should  include  the  following  tools : 

1st.  Triangles,  ruling  pen,  compass,  bow  pen,  bow  pencil, 
dividers  large  and  small,  pen  knife,  pen  wiper,  scales,  oil 
stone,  etc. 

2nd.     A  copy  of  some  rolling-mill's  handbook. 

3rd.  Tables  of  squares  and  longarithms  of  dimensions  in 
feet,  inches  and  fractions. 

4th.     A  copy  of  the  office  standards. 

5th.  A  five  place  table  of  the  natural  functions  of  angles 
varying  by  minutes. 

6th.  A  five  place  logarithmic  table  of  numbers  and  func- 
tions of  angles. 

7th.     A  slide  rule. 

8th.     Reference  books. 

9th.  The  following  which  are  usually  supplied  by  the 
office :  drawing  tables,  drawing  boards,  T-squares,  erasers,  soap- 
stone,  pencils,  pens,  tacks,  tracing  cloth,  drawing  paper,  ink, 
and  chalk. 

The  drawing  instruments  should  be  of  the  best  quality. 
Loss  of  time  due  to  poor  instruments  is  inexcusable.  Triangles 
should  be  transparent  and  not  less  than  TV  inches  thick.  A 
5  in.  or  6  in.,  45  degree  triangle  and  an  8  in.  or  10  in.  30-60  de- 
gree triangle  will  be  found  convenient.  For  some  classes  of 
work  a  quarter  pitch  triangle  (slope  1  in  2)  and  a  small  triangle 
that  will  fit  the  standard  bevel  of  the  flanges  of  I-beams  and 


Art.  25.  A  DRAFTSMAN'S  EQUIPMENT.  49 

channels  (1  in  6)  will  save  time.  The  ruling  pen  should  be  of 
a  kind  that  is  easily  cleaned  because  the  ink  used  dries  rapidly. 
There  are  pencil  sharpening  machines  which  do  very  good  work. 
If  there  is  not  one  conveniently  located  in  the  office,  a  sharp  pen 
knife  can  be  made  to  do  good  work  in  connection  with  a  piece 
of  sand  paper  or  a  file  for  sharpening  the  lead.  A  draftsman 
who  wishes  to  make  a  workmanlike  drawing  will  not  work  with 
a  blunt  pointed  pencil. 

The  architects'  scale  is  used  for  all  shop  drawings.  This  is 
a  scale  of  feet  and  inches.  Scales  should  not  be  over  6  inches 
long  for  detail  work  and  preferably  have  white  celluloid  faces. 
A  long  scale  necessitates  moving  the  T-square  and  triangles  too 
much.  A  12  inch  decimal  scale  for  longer  dimensions  and 
graphic  calculations  should  also  be  provided.  A  triangular  ar- 
chitects' scale  is  usually  divided  into  the  following  scales  per 
foot :  3-32  in.,  %  in.,  3-16  in.,  %  in.,  %  in.,  i/2  in.,  %  in.,  1  in., 
~Ly2  in.,  3  in.  and  12  in.  or  full  size.  As  most  of  these  scales  are 
used  infrequently,  it  is  more  convenient  to  have  two  flat  scales 
covering  the  more  often  used  scales.  One  divided  into  scales 
of  y8  in.,  14  in.,  %  in.  and  1  in.  per  foot  and  another  divided 
into  %  in.,  %  in.,  iy2  in.  and  3  in.  per  foot  will  answer  most 
purposes.  A  scale  of  1*4  in.  per  foot  makes  a  very  nice  scale 
for  some  classes  of  work  but  it  is  not  a  standard  scale.  The  scale 
of  14  in.  per  foot  is  much  used  by  architects. 

A  good  pencil  eraser,  one  that  will  not  "smear,"  is,  of 
course,  necessary.  Ink  on  tracings  should  be  erased  with  a 
rubber  ink  eraser  although  a  steel  eraser  (knife)  may  be  used 
occasionally.  To  prevent  ink  "running"  and  dirt  accumulating 
on  the  spot  which  has  been  rubbed,  the  tracing  cloth  should  be 
rubbed  with  soapstone.  To  confine  the  rubbed  surface  within 
the  required  limits,  it  is  convenient  to  have  a  thin  metal  erasing 
shield  with  holes  arid  slots  of  different  sizes. 

The  ink  should  be  waterproof  india  ink  of  good  quality. 

For  drawing  lines  on  detail  paper  a  6H  pencil  should  be 
used,  because  it  does  not  require  such  frequent  sharpening  as  a 
softer  pencil.  For  putting  in  dimensions  and  figures  a  4H  pencil 
will  be  about  right.  On  tracing  cloth  a  3H  pencil  will  work  best, 
and  a  soft  pencil  is  needed  for  scratch  figuring. 

A  pen  must  be  "broken  in"  before  good  lettering  can  be 


50  A  DRAFTSMAN'S  EQUIPMENT.  Art.  25 

done  with  it.  After  it  'has  been  used  for  some  time  the  point 
becomes  blunt  and  may  be  improved  by  using  a  knife  on  it  as 
on  a  pencil  in  sharpening  it. 

The  rolling-mill  hand  books  contain  much  information  of 
use  to  the  draftsman,  and  he  should  know  what  may  be  found 
in  them.  The  pages  most  frequently  referred  to  should  be  in- 
dexed for  quick  reference  in  some  manner  similar  to  a  ledger 
index.  The  principal  shapes  rolled  by  the  various  mills  are  all 
alike  and  in  accordance  with  the  standard  adopted  by  the  Manu- 
facturers' Association.  All  properties  of  these  shapes  are  given 
in  the  hand  books.  The  American  Bridge  Company's  Stand- 
ards give  much  other  valuable  information. 

Each  office  usually  has  a  set  of  standard  tables  and  draw- 
ings. Many  of  these  are  of  general  value,  but  some  correspond 
with  certain  local  shop  practices. 

Tables  of  squares  and  logarithms  of  dimensions  in  feet  and 
inches  are  in  constant  use,  and  are  a  much  greater  help  than 
would  appear  on  first  thought.1  In  working  with  right  angle 
triangles,  only  the  table  of  squares  is  necessary.  The  table  of 
logarithms  is  not  used  so  often,  but  when  there  is  use  for  it 
it  saves  much  time.  These  tables  give  results  to  the  nearest  1-32 
of  an  inch,  and  this  is  the  smallest  fraction  ever  used  on  struc- 
tural steel  drawings. 

The  above  tables,  together  with  a  good  table  of  the  natural 
functions  of  angles  such  as  is  given  in  Trautwein's  Pocket- 
book,  and  a  five  place  table  of  logarithms  such  as  Gauss's  or 
'Jones'  will  enable  the  draftsman  to  solve  all  problems  in  men- 
suration which  may  arise,  if  he  is  thoroughly  familiar  with  the 
fundamentals  of  geometry  and  trigonometry. 

The  draftsman  should  be  familiar  with  the  use  of  the  slide 
rule,  and  should  use  it  to  calculate  pins,  rivets,  bearings,  etc. 
(18)  If  the  office  is  provided  with  a  Thacher  Cylindrical  Rule 
it  may  be  used  to  good  advantage  in  calculating  the  dimensions 


114 Tables  of  Squares,"  by  John  L.  Hall  and  "Buchanan's  Tables  of 
Squares,"  by  E.  E.  Buchanan,  give  the  squares  of  dimensions  under 
50  feet,  expressed  in  feet  and  inches.  Tables  by  Thos.  W.  Marshall 
give  the  logarithms  of  the  same  quantities.  ^Smoley's  Tables  of 
Squares  and  Logarithms,"  by  Constantine  Smoley,  give  both  the 
squares  and  logarithms  of  these  dimensions  in  parallel  columns. 


Art.  26.  ORDERING  MATERIAL.  61 

in  oblique  triangles,  and  will  give  results  within  1-32  of  an  inch 
so  long  as  none  of  the  lengths  involved  exceed  about  30  feet. 

A  note  book  is  very  convenient  for  keeping  calculations 
which  one  may  wish  to  refer  to  again.  Many  figures  which  a 
draftsman  makes  will  be  on  scratch  paper,  but  all  figures  which 
may  be  needed  for  future  reference  and  for  consultation  when 
the  changes  made  by  the  checker  are  gone  over,  should  be  kept 
in  a  permanent  and  methodical  form.  A  careful  man  will  find 
satisfaction  in  seeing  how  he  made  a  mistake,  and  this  record 
will  also  be  valuable  in  giving  reasons  for  certain  things  he  has 
done,  and  prevent  his  being  misled  by  some  one  who,  perhaps, 
has  not  considered  all  the  conditions. 

A  draftsman  should  have  at  hand  reference  books  in  order 
that  he  may  look  up  any  point  in  theory  with  which  he  is  not 
familiar.  A  few  may  be  mentioned  here  but,  of  course,  for 
structures  out  of  the  ordinary  special  works  should  be  consulted. 
The  most  useful  are: 

Johnson's  "Theory  and  Practice  of  Modern  Framed  Struc- 
tures," Heller's  "Stresses  in  Structures,"  some  good  work  on 
the  strength  of  materials,  Wright's  "The  Designing  of  Draw 
Spans,"  Freitag's  "Architectural  Engineering,"  Merriman  and 
•Jacoby's  "Bridge  Design"  (Part  III  of  Roofs  and  Bridges), 
Kent's  "Mechanical  Engineer's  Pocketbook,"  Trautwein's 
"Civil  Engineer's  Pocketbook,"  Engineering  News,  etc.  Access 
to  the  Transactions  of  the  American  Society  of  Civil  Engineers, 
and  of  other  engineering  societies  will  be  valuable.  An  indivi- 
dual card  index  should  be  kept  in  order  that  any  subject  may 
be  looked  up  when  occasion  requires. 

26.  Ordering  Material.  As  soon  as  a  contract  has  been 
secured  and  entered,  complete  data  relating  to  the  construction 
are  turned  over  to  the  drafting  department.  The  first  thing  to 
be  done  by  this  department  is  to  prepare  a  list  of  the  material 
required,  which  is  called  an  "order  bill."  The  draftsman  to 
whom  this  is  entrusted  should  first  carefully  examine  all  data. 
If  any  necessary  information  is  found  lacking  at  any  point  in 
the  progress  of  the  work,  it  should  be  promptly  reported.  Care 
should  be  taken  to  include  everything  in  the  order  bill  that  will 
be  required  to  make  the  structure,  unless  upon  inquiry  it  is 
found  that  certain  materials  may  be  ordered  later. 


52  ORDERING  MATERIAL.  Art.  26 

Since  the  order  bill  must,  in  general,  include  all  details  such 
as  pin  plates,  batten  plates,  lacing  bars,  rollers,  pins,  eye  bars, 
rods,  timber,  lead,  corrugated  iron,  windows,  doors,  crane  run- 
way rails,  etc.,  it  is  necessary  to  proportion  all  details,  to  calcu- 
late pins,  rivets,  bearings  and  connections,  and  to  determine 
clearances,  splices,  etc.  In  some  cases  considerable  drafting 
will  be  required,  but  not  nearly  so  much  as  will  be  necessary  to 
make  complete  detail  drawings.  In  general,  this  preliminary 
drafting  should  be  done  so  that  after  the  order  bill  is  complete 
the  drawings  may  be  developed  into  final  shop  drawings.  This 
method  will  save  much  drafting,  which  is  expensive  work. 

In  order  to  expediate  the  placing  of  the  orders  for  the  ma- 
terial at  the  mills,  no  more  drafting  than  necessary  should  be 
done.  It  may  be  supplemented  by  free  hand  sketches  and  notes, 
which  should  be  preserved  with  other  data  for  reference  by  the 
checker  and  draftsman  making  the  shop  drawings. 

For  a  contract  of  any  magnitude  the  order  bills  would  be 
gotten  out  in  sections;  those  parts  which  will  be  needed  first 
should  be  gotten  out  first.  In  any  case,  the  first  attention  should 
be  given  to  the  kind  of  material  which  will  be  most  difficult  to 
get  promptly. 

However,  time  spent  upon  a  consideration  of  the  entire  con- 
tract in  all  its  bearings,  and  especially  with  regard  to  duplica- 
tion of  parts,  is  never  wasted. 

The  order  bills  are  checked  and  a  copy  sent  to  the  order 
department.  The  originals  are  retained  for  the  guidance  of  the 
draftsmen  who  make  the  shop  drawings.  The  element  of  time 
is  so  important  that  most  companies  do  not  make  blue  prints 
of  the  order  bills  but  use  some  more  rapid  duplicating  process. 

The  order  department  makes  up  a  "mill  order"  from  the 
order  bills,  bringing  together  all  items  of  the  same  kind  and 
combining  some  of  the  shorter  lengths  into  long  lengths  (mul- 
tiple lengths)  to  be  sheared  to  the  proper  lengths  at  the  shop. 

•Some  companies  keep  more  or  less  material  in  stock  in 
order  to  be  able  to  make  prompt  deliveries  of  certain  classes 
of  work.  In  this  way  considerable  waste  (short  pieces)  accumu- 
lates, which  must  be  applied  on  contracts  whenever  an  oppor- 
tunity offers.  It  is  the  duty  of  the  order  department  to  keep 
track  of  the  stock,  to  keep  up  the  supply  of  stock  sizes,  and  not 


Art.  26.  ORDERING  MATERIAL.  63 

to  allow  an  accumulation  of  waste.  When  stock  material  is  ap- 
plied to  a  contract  it  should  be  so  marked,  in  order  that  it  may 
be  reserved.  The  shop  bill  generally  shows  what  items  are  to 
come  from  the  mill  and  what  items  from  stock.  Stock  material 
cannot  always  be  used  on  contracts,  as  some  specifications  re- 
quire a  different  quality  of  material  from  that  carried  in  stock 
and  require  inspection  at  the  mills. 

The  importance  of  avoiding  errors  and  omissions  in  the 
order  bills  is  apparent,  since  they  may  cause  serious  delay  to  the 
entire  work. 

In  making  up  the  order  bill,  it  should  be  remembered  that 
odd  sizes  of  angles  'and  other  shapes  should  be  avoided  in  order 
to  get  prompt  delivery  from  the  mill.  %  inch  extra  material 
should  be  ordered  for  all  tool  finished  (milled  or  planed)  sur- 
faces, except  for  the  flat  surfaces  of  plates  for  which  1-16  in.  or 
y8  in.  extra  should  be  ordered,  depending  upon  the  size  of  the 
plate.  Stiffener  angles  which  are  to  be  crimped  or  offset,  are 
usually  ordered  as  long  as  the  depth  back  to  back  of  angles  of 
the  girder  to  which  they  belong.  The  length  of  bent  angles  and 
plates  is  taken  on  the  center  of  gravity  line.  Other  material  is 
ordered  the  exact  length  required  (avoiding  smaller  fractions 
than  eighths  of  an  inch)  and  usually  comes  a  little  longer  so 
that  it  may  be  sheared  to  the  finished  length. 

Plates  are  of  two  kinds,  "sheared"  and  "universal  mill." 
The  former  have  sheared  edges  and  the  latter  rolled  edges.  The 
maximum  width  of  universal  mill  plates  varies  from  20  in.  to 
48  in.,  depending  upon  the  mill  where  they  are  rolled.  In  the 
rolling  mill  handbooks  will  be  found  tables  showing  the  maxi- 
mum length  to  which  plates  of  various  widths  and  thicknesses 
can  be  rolled.  Plates  up  to  7  in.  in  width  are  called  bars.  Flange 
plates  for  plate  girders  are  usually  obtained  as  long  as  wanted, 
but  web  plates  must  be  spliced.  It  is  usual  to  order  web  plates 
of  a  width  !/£  in.  less  than  the  depth  back  to  back  of  angles,  and 
to  allow  y±  in.  clearance  between  their  ends.  It  is  permissable 
to  order  odd  shaped  plates  sheared  to  the  dimensions  wanted,  as 
shown  by  a  sketch. 

Angles  may  be  obtained  in  single  pieces  up  to  about  90  feet 
long,  provided  that  they  do  not  weigh  more  than  about  3,000  Ibs. 
apiece.  Special  sizes  should  be  avoided  on  account  of  slow  de- 


54  SHOP  DRAWINGSo  Art.  27 

livery.  The  order  bill  should  indicate  the  kind  of  material 
(soft  or  medium)  and  the  specifications  governing  its  quality 
and  inspection. 

27o  Shop  Drawings.  Drawings  should  be  made  on  the 
dull  side  of  tracing  linen,  because  they  will  not  lie  flat  when 
made  on  the  smooth  side.  An  experienced  draftsman  will  work 
directly  on  the  tracing  cloth  and  this  cannot  be  done  except  on 
the  dull  side.  Drawings  may  be  fastened  to  the  board  with 
thumb  tacks,  but  it  will  be  found  more  satisfactory  to  use  very 
small  carpet  tacks,  tacking  the  four  edges  like  a  carpet  so  that 
the  drawing  will  be  stretched  and  present  as  smooth  a  surface 
as  possible.  Changes  in  temperature  and  moisture  of  the  air 
may  sometimes  necessitate  restretching.  The  drawing  should  be 
covered  up  at  night  with  a  heavy  cloth  or  a  piece  of  table  oil 
cloth.  If  the  drawing  is  made  on  the  tracing  linen  direct,  the 
principal  lines  may  be  inked  before  the  drawing  is  completed 
in  pencil.  This  will  bring  out  the  main  parts  and  make  it  more 
satisfactory  to  work  with,  especially  if  there  is  much  work  on 
the  drawing,  as  the  lines  are  liable  to  become  faint  from  rubbing 
over  them.  It  is,  however,  safer  for  an  inexperienced  man  to 
make  a  complete  pencil  drawing  before  doing  any  inking. 

In  order  that  the  tracing  cloth  may  "take"  the  ink  it  is 
necessary  to  rub  it  with  pulverized  chalk,  Fuller's  earth,  or 
blotting  paper.  This  is  especially  necessary  during  cold  and 
damp  weather. 

The  draftsman  should  not  get  the  idea  that  the  appearance 
of  a  shop  drawing  is  of  no  importance.  A  drawing  should  have 
a  workmanlike  appearance  or  it  will  not  inspire  confidence  in 
its  correctness.  The  general  arrangement  and  the  lettering  are 
the  main  features  so  far  as  appearance  is  concerned.  All 
lettering  should  be  free  hand  and  the  draftsman  should,  at  the 
beginning,  practice  with  exceeding  patience  some  simple  style 
of  lettering. 

The  style  used  in  the  drawings  published  in  the  Engineering 
News  is  a  very  good  one  to  follow.  A  very  important  point  is 
to  have  the  letters  and  figures  of  different  sizes,  depending  upon 
their  importance.  The  sizes  of  materials  should  be  more  promi- 
nent than  the  rivet  spacing,  and  center  lengths  than  secondary 
dimensions.  There  is  also  a  beet  position  for  each  dimension. 


Art.  27  SHOP  DRAWINGS  55 

The  letters  and  figures  should  be  made  as  carefully  as  is  con- 
sistent with  rapidity.  It  is  only  practice,  persistent  and  patient, 
that  can  make  a  good  letterer.  Not  all  can  hope  to  become  equally 
proficient,  but  all  can  improve. 

The  general  appearance  of  a  drawing  depends  very  much 
upon  the  general  arrangement,  the  scale,  and  the  relative  sizes 
of  letters.  A  drawing  may  cover  practically  all  the  available 
space  within  the  border  lines,  if  there  is  no  evidence  of  crowding 
anywhere,  and  if  the  various  parts  or  pieces  represented  stand 
out  clearly  so  that  the  different  views  of  the  several  pieces  can 
not  be  confused.  There  is  an  advantage  in  compactness,  but 
clearness  is  the  first  consideration.  Not  every  one  who  uses  a 
drawing  can  read  it  as  readily  as  the  man  who  made  it.  HE 
SHOULD  MAKE  IT  SO  PLAIN  THAT  IT  WILL  EXPLAIN  ITSELF 
AND  THAT  ONLY  GROSS  NEGLIGENCE  WILL  ALLOW  ANYONE 
TO  MAKE  A  MISTAKE  IN  USING  IT. 

The  object  should  be  not  to  make  it  "good  enough"  but  to 
make  it  first  class. 

The  length  of  a  structure,  like  a  truss,  seldom  determines 
the  scale  of  the  drawing.  Usually  the  available  width  of  a  sheet 
determines  the  scale  to  be  used.  If  the  structure  is  too  long  to 
show  on  one  sheet  to  this  scale  two  or  more  sheets  may  be  used. 
The  center  line  diagrams  of  trusses  are  usually  drawn  to  a 
smaller  scale  than  the  details,  say  %  in-  or  %  in.  per  foot  while 
the  details  would  be  1  in;  or  1%  in.  per  foot.  In  this  case,  of 
course,  there  is  a  part  of  the  member  near  the  middle  which  is 
cut  out  and  which  need  not  be  shown,  but  the  spacing  of  rivets, 
etc.,  is  indicated.  True  projections  are  not  always  made  if  they 
do  not  serve  to  make  matters  clear.  Bottom  views  are  seldom 
made  but  sections  instead,  placed  below  the  elevation.  The  top 
view  should  always  be  above  the  elevation.  A  half  top  view 
and  half  section  are  sometimes  made  together  when  symmetry 
will  allow.  A  single  view  or  two  views  will  sometimes  suffice, 
especially  if  it  is  a  construction  with  which  the  shop  is  familiar. 
There  should  be  no  more  drafting  than  is  necessary  for  clear- 
ness. 

Drawings  should  have  one  or  two  plain  "border  lines.  If  two 
are  used  the  blue  prints  may  be  trimmed  to  the  outer  one.  ( See 
Fig.  24.)  In  some  drafting  rooms  an  outfit  for  printing  titles 


56 


SHOP  DRAWINGS. 


Art.  27 


on  tracings  is  used ;  in  some  rubber  stamps  are  used.  Printing 
is  the  most  satisfactory  method  when  the  number  of  drawings 
turned  out  is  large.  Titles  should  correspond  with  some  stand- 
ard as  indicated  in  Fig.  24.  The  title  should,  when  possible,  be 
in  the  lower  right  hand  corner.  When  necessary  it  may  be 
divided  in  two  parts  placed  side  by  side.  A  supplementary 
form  for  general  information  is  frequently  placed  in  the  lower 
left  hand  corner  as  shown  in  Fig.  25. 

3(5* 


THE  OHIO  STATE  BRIDGE  CO. 
COLUMBUS,  OHIO 

Bridge  No.34  Western  Div.QRAM.Ry 

I  Through  Truss  Spon-Doyb/eTrcrd(,Stew 


Floor  Beams  Stringers  and 
Portals. 

In  Charge  of  Smith 
Drawn  by  AJ.K.  7-/-07     Revised  8-6-O7 
Checked  by  JWT7-24.-07  Revised  8-7-07 

Shop  Bills  Nos.  l£3d  4- 

CONT.   NO.  746 


e  Print  on  Mis  Line)' 


(7r/m  Tracing  on  ffj/s  Line) 


Fig.  24. 

Dimension  lines  and  rivet  gage  lines  should  be  very  fine 
and  preferably  made  with  black  ink.  They  are  sometimes  made 
with  red  ink,  but  the  ink  should  be  of  known  quality  in  order 
that  it  may  not  run  or  spread  with  age.  Center  lines  which 
form  one  end  of  a  view  should  be  heavy  dot  and  dash  lines; 
other  center  lines  should  be  fine  lines.  No  shading  is  attempted 
on  shop  drawings  except  to  show  curved  surfaces. 

All  lines  of  dimensions  should  connect  completely  with  the 
centers,  and  there  should  be  separate  lines  for  center  distances, 
rivet  spacing,  lacing  spacing,  etc. 


Art.  27. 


SHOP  DRAWINGS. 


57 


Rivets  connecting  lacing  bars  to  compression  members 
should  stagger  with  those  in  the  web  of  the  member.  The  end 
bars  should  connect  to  the  first  rivet  in  the  batten  plate  or  one 
not  over  5  in.  from  this  rivet.  Batten  plates  should  be  made  of 
such  widths  as  will  fit  the  spacing  of  the  lacing  and  meet  the 
requirements  of  the  specifications. 

.  _    36" 


.  /9O/. 


Mater/a/  <$off  O.  H.STeel. 


-    none. 


Shop  Painf- 


Fig.  25. 

Dimensions  which  determine  clearances  for  field  connec- 
tions, the  position  of  open  holes,  etc.,  should  be  given  in  such  a 
manner  as  to  be  convenient  for  the  inspector.  It  should  not  be 
necessary  for  him  to  add  rows  of  figures.  If  the  inside  distance 
at  the  end  of  a  member  is  the  important  one  for  clearance,  that 
should  be  given.  If  the  member  is  to  be  entered  inside  of  an- 
other, its  outside  width  should  be  given.  In  some  cases  both  are 
necessary. 

For  identification  in  the  drawing  room,  shop  and  field,  each 
piece  should  have  a  mark.  All  pieces  which  are  exactly  alike, 
should  have  the  same  mark.  The  marks  should  all  appear  on 
the  general  marking  diagram,  or  erection  plan,  which  shows  the 
relative  location  of  all  the  pieces  by  their  marks. 

Under  the  drawing  of  each  piece  the  number  required 
should  be  plainly  given  together  with  the  numbers  which  are 
to  be  right  and  left,  thus, 

2  Right  Girders  Req.    Mark  G  R  (shown) 
2  Left  Girders  Req.    Mark  G  L. 


68  SHOP  DRAWINGS.  Art.  27 

The  system  of  marking,  for  each  kind  of  Structure,  should 
be  standard  as  far  as  possible.  For  example,  U  might  always 
stand  for  upper,  L  for  lower,  P  for  portal,  V  for  vertical,  D  for 
diagonal,  B  for  bracket,  S  for  stringer,  F  for  floor  beam,  etc. 
Marks  should  be  as  simple  as  possible,  and  preferably  consist  of 
capital  letters  and  figures,  avoiding  primes  and  subscripts.  To 
insure  shipment,  small  pieces  which  the  drawings  show  bolted 
to  large  ones,  may  be  given  separate  marks  and  noted  on  the 
shipping  bill. 

Steel  in  section  is  shown  by  uniform  cross  hatching  or  in 
black.  See  Figs.  26,  28,  and  29.  Other  kinds  of  material  are 
seldom  used  except  for  draw-bridge  machinery.  If  some  con- 
vention is  adopted  for  each  kind  of  material,  it  will  serve  to 
make  the  drawing  clearer. 

It  is  well  to  follow  some  conventions.  If  a  member  is  ver- 
tical in  a  structure,  it  should  be  drawn  with  its  axis  parallel 
with  the  sides  of  the  drawing  unless  this  would  necessitate  the 
use  of  too  small  a  scale,  in  which  case  it  may  be  drawn  parallel 
with  the  top  of  the  drawing,  with  the  top  of  the  piece  at  the 
right.  Inclined  members,  when  not  shown  in  their  natural  posi- 
tion, should  be  drawn  lengthwise  of  the  sheet. 

Notes  may  be  used  when  they  will  save  considerable  draft- 
ing, but  should  generally  be  'avoided.  Making  the  drawing  com- 
plete will  guard  against  mistakes  in  the  office  and  the  shop. 
A  note  should  be  so  worded  that  its  meaning  cannot  possibly  ~be 
mistaken.  It  is  not  permissable  to  refer  to  a  reference;  the 
drawing  referred  to  should  give  full  information.  In  any  case 
each  drawing  should  give  sizes  of  all  material,  pin  sizes,  center 
dimensions,  and  other  important  information. 

Duplication  in  details,  in  spacing,  in  parts  of  members  and 
in  members  is  very  important.  The  number  of  templets  is  by 
this  means  reduced  to  a  minimum.  It  is  permissable  to  use  a 
little  extra  material  to  obtain  duplication  in  some  cases.  When 
two  members  differ  but  slightly  from  each  other,  one  drawing, 
with  proper  notes,  will  answer  for  both.  If  two  drawings  are 
necessary  and  some  parts  of  one  are  the  same  as  for  the  other, 
it  is  better  not  to  repeat  the  rivet  spacing  but  to  refer  to  the 
other  drawing,  as  this  will  call  attention  to  the  fact  that  there 
is  a  duplication  of  templets.  A  templet  is  frequently  made  to 


Art.  27.  SHOP  DRAWINGS.    .  69 

answer  for  two  different  pieces  by  putting  into  it  all  the  holes 
for  each  piece  and  marking  one  set  of  holes  in  some  way  to 
distinguish  them  from  the  other  set. 

Rivet  Spacing  should  be  as  regular  as  possible.  All  rivet 
heads  need  not  be  shown  but  they  should  not  be  omitted  at  the 
ends  of  members,  where  clearances  are  important,  in  pin  plates, 
or  where  countersinking  or  flattening  are  needed.  Field  holes 
should  always  be  shown  blackened,  and  it  is  generally  a  good 
thing  to  show  them  in  at  least  two  views.  The  conventional 
signs  for  countersinking  and  flattening  (See  Fig.  20)  should  be 
made  very  plain  lest  they  be  confused  with  dimension  lines.  No 
countersinking  is  allowed  in  the  tension  flanges  of  stringers, 
floor  beams  or  girders.  All  countersinking  should  be  avoided 
in  long  pieces  since  it  involves  an  extra  shop  operation  and  long 
pieces  are  expensive  to  handle. 

All  open  holes  should  be  so  located  that  the  field  rivets 
may  be  easily  driven.  Rivets  are  driven  from  the  sides  or  from 
above,  never  from  below.  It  is  not  good  practice  to  put  two 
consecutive  rivets  on  the  same  line  in  an  angle  having  two  gage 
lines,  except  for  purposes  of  symmetry,  and  when  it  cannot  be 
avoided,  as  in  the  connection  of  a  floor  beam  to  a  girder. 

Punching  of  holes  of  different  sizes  in  the  same  piece  should 
be  avoided  as  much  as  possible,  especially  in  long  pieces,  because 
it  requires  extra  handling.  Avoid  two  or  more  shearings  at  the 
end  of  an  angle  or  the  edge  of  a  plate  when  one  will  answer 
just  as  well.  Projecting  corners  should,  however,  not  be  al- 
lowed. Whenever  a  reentrant  cut  has  to  be  made,  there  should 
be  no  sharp  angle  but  a  curve. 

In  giving  dimensions  over  9  inches  the  feet  and  inches 
should  generally  both  be  given,  thus  O'-ll",  3'-7".  All  dimen- 
sions over  one  foot,  except  the  widths  of  plates,  should  be  given 
in  feet  and  inches;  width  of  plates  are  always  given  in  inches, 
thus,  1— 37"X%"X3'— 6y2".  The  longer  leg  of  an  angle  should 
be  given  first.  Rivet  spacing  should  not  be  given  by  repeating 
a  number  of  consecutive  spaces  that  are  just  alike,  but  should 
be  indicated  as  follows: 

8  spaces  at  3"=2'-0" 

8  alternate  spaces  at  V— 3"=10'— 0". 


60  SHOP  DRAWINGS.  Art.  27 

Unless  the  stringers  rest  on  the  bottom  flange  of  the  floor 
beam,  shelf  angles  should  be  provided  for  them  to  rest  on  for 
convenience  in  erecting.  Where  stringers  rest  on  the  bottom 
flanges  of  the  floor  beams,  and  where  inside  splice  angles  are 
used,  they  should  be  ground  to  fit  the  fillet  of  the  flange  angle. 

If  angle  laterals  are  used,  which  have  lugs  riveted  to  them, 
it  is  easiest  to  make  the  back  of  the  angle  the  center  line. 

It  should  be  remembered  that  angles  are  not  exactly  of  the 
nominal  size,  but  that  the  length  of  the  legs  overruns,  except  for 
sizes  rolled  in  finishing  rolls.  Making  fillers  and  splice  plates 
1/4  inch  shorter  than  the  nominal  distance  between  flange  angles 
will  not  always  answer. 

Entering  connections  should  be  avoided.  They  make  erec- 
tion expensive  and  are  liable  to  result  in  injury  to  the  material. 

Wherever  two  or  more  members  come  together,  clearance 
should  be  allowed  if  possible.  The  thickness  of  an  eyebar  head, 
if  figuring  clearances,  is  always  taken  TV  inch  greater  than  the 
nominal  thickness.  A  total  further  clearance  of  i/4  inch  to  % 
inch  is  allowed  where  several  members  enter  between  the  sides 
of  another,  the  amount  depending  upon  the  members  so  enter- 
ing, the  number  of  pin  plates,  etc.  Pin  fillers  are,  for  the  same 
reason,  made  14  inch  shorter  than  the  space  they  are  to  fill. 

Projecting  plates  should  not  be  riveted  to  large  pieces,  but 
shipped  loose.  It  is  better  to  drive  a  few  more  rivets  in  the 
field  than  to  have  these  details  broken  off  in  shipping  and  hand- 
ling, or  have  them  interfere  with  the  handling  of  heavy  pieces. 
Lateral  plates  for  plate  girder  spans  may  be  riveted  to  one  of 
the  laterials  connecting  to  them  if  the  laterals  are  not  too  long. 

Care  should  be  exercised  so  that  no  part  of  the  lateral  sys- 
tem will  interfere  with  the  floor  construction  or  the  masonry. 

It  is  important  to  know  in  what  order  the  spans  of  a  via- 
duct will  be  erected  and  to  arrange  the  details  at  the  tops  of 
the  columns  so  that  each  span  may  be  put  up  independently. 

Holes  for  anchor  bolts  must  be  so  located  that  the  masonry 
may  be  drilled  after  the  steel  work  is  in  place. 

At  panel  points,  not  only  those  rivets  which  come  opposite 
a  member  in  its  final  position  should  be  flattened  or  countersunk 
for  clearance,  but  also  enough  to  allow  the  members  to  be  easily 
assembled.  Batten  plates  should  not  come  too  close  to  a  diago- 
nal member. 


Art.  27.  SHOP  DRAWINGS.  61 

Top  chord  splices  should  come  opposite  each  other  in  the 
two  trusses,  and  the  sections  nearest  the  center  should  extend 
over  at  least  two  panel  points  so  that  in  erection  this  panel  will 
be  self-supporting1.  It  should  be  remembered  that  the  traveler 
must  be  moved  and  cannot  generally  support  pieces  except  for 
about  one  panel  length. 

There  are  two  general  methods  of  making  shop  drawings. 
First,  a  structure  or  part  of  a  structure  may  be  drawn  showing 
all  parts  assembled  in  their  proper  relative  positions.  A  bridge, 
for  example  may  be  drawn  showing  the  truss  members  (usually 
half  of  one  truss  for  a  square  span)  in  the  relative  positions  in 
which  they  belong,  while  a  separate  drawing  is  made  of  each 
of  the  other  pieces  such  as  floor  beams,  portals,  etc.  This  method, 
of  course,  is  not  adapted  to  some  things,  like  floors  and  columns 
of  office  buildings.  Second,  each  kind  of  piece  belonging  to  a 
structure  is  drawn  separately  and  complete  in  itself.  In  the 
case  of  a  truss  for  example,  this  necessitates  the  making  of  a 
layout  of  each  joint  beforehand,  in  order  to  determine  clear- 
ances, and  the  fitting  together  of  the  parts.  This  method  re- 
quires more  drafting  than  the  first,  and  is  therefore  more  expen- 
sive. The  first  method  is  nearly  always  used  for  bridge  and  roof 
trusses  unless  the  depth  is  so  great  that  it  would  necessitate  too 
small  a  scale. 

At  some  plants  the  templet  shop  is  arranged  to  permit  lay- 
ing out  a  structure  full  size.  The  templet  maker  locates  the 
rivets  which  are  shown  but  not  exactly  located  on  the  drawing. 
Where  this  is  practiced  drawings  -are  made  in  a  somewhat  dif- 
ferent manner,  as  to  what  dimensions  are  given,  than  where  all 
details  including  rivet  spacing  are  shown. 

The  beginner  should  always  have  a  sample  of  the  kind  of 
structure  of  which  he  is  required  to  make  a  drawing,  for  a 
guide.  There  are  many  practical  points  which  can  only  be 
picked  up  in  this  way.  He  should  also  make  himself  familiar 
with  the  machines  in  the  shop  and  their  capacities.  It  is  some- 
times as  easy  to  design  a  masonry  plate  which  will  go  into  the 
planer  as  one  that  is  too  wide  for  it. 

Before  starting  on  the  drawings  for  any  particular  struc- 
ture, a  draftsman  should  make  himself  perfectly  familiar  with 
all  the  data.  Time  spent  in  a  general  preliminary  consideration 


62  ORDER  OF  PROCEDURE.  Art.  28 

and  plan  of  action  is  generally  well  spent.  If  further  informa- 
tion is  required,  it  should  be  asked  for  at  once.  If  a  mistake  or 
omission  is  discovered  in  the  order  bill,  the  attention  of  the 
engineer  in  charge  of  the  office,  or  of  this  particular  contract, 
should  be  called  to  it  at  once. 

Working  to  the  order  bill  may  make  some  trouble,  but  this 
is  necessary.  Should  any  doubtful  points  come  up,  some  one 
should  be  consulted  who  is  more  familiar  with  this  kind  of  work, 
or  with  the  requirements  of  the  parties  for  whom  the  work  is 
to  be  built.  A  man  should  never  ~be  ashamed  to  ask  intelligent 
questions. 

28.      Order  of  Procedure  for  a   Pin   Connected   Bridge. 

No  definite  order  of  procedure  can  be  outlined,  which  can  be 
followed  in  all  cases,  but  the  following  order  for  a  pin  connected 
truss  bridge  will  serve  as  a  guide  to  the  beginner. 

The  stress  sheet  and  specifications  form  a  part  of  the  con- 
tract and  the  draftsman  must  work  from  these. 

1st.  Write  on  a  blue  print  of  the  stress  sheet  the  horizontal 
and  vertical  components  of  the  stresses  in  the  inclined  members. 

2nd.  Determine  the  location  of  the  centers  of  gravity  of 
the  compression  members  and  decide  on  the  location  of  the 
center  lines. 

3rd.  Determine  all  the  center  lengths  so  as  to  give  the 
required  camber. 

4th.    Make  a  table  of  heights  as  follows : 

Depth  of  tie  over  the  stringers  = 

Depth  of  the  stringers  = 

Bottom  of  stringer  to  Bot.  of  Fl.  Bm.  = 
Bottom  of  Floor  Bm.  to  Pin  Cent.        = 


Base  of  Rail  to  Pin  Gent.  =  (Sum) 

Pin  Cent,  to  Masonry  = 


Base  of  Rail  to  Masonry  =  (Sum) 

Lower  Pin  Cent,  to  Base  of  Rail 
Required  Clearance  = 


Lower  Pin  Cent,  to  Clearance  =  (Sum) 

Depth  of  Truss  C.  to  C.  Pins  = 


Depth  of  Portal,  Vert,  from  P.  C.         =  (Diff.) 


Art.  28.  ORDER  OF  PROCEDURE.  68 

5th.  If  the  bridge  is  on  a  skew,  calculate  the  lengths  and 
bevels  necessary  to  draw  the  portal. 

6th.  Calculate  the  size  of  masonry  plate  required  so  as 
not  to  exceed  the  allowed  pressure  on  the  masonry  and  so  as  to 
provide  enough  room  for  the  rollers. 

7th.  Assume  sizes  of  pins,  determine  thicknesses  of  pin 
bearings  on  each  member  and  calculate  the  pins.  When  the  pins 
are  all  calculated  decide  upon  two  or  three  sizes  for  the  truss, 
making  some  larger  than  necessary  for  the  sake  of  simplicity. 
Fix  on  the  location  and  thicknesses  of  all  pin  plates  and  the 
number  of  rivets  required  in  each.  The  calculation  of  the  pins 
will  have  determined  the  packing  at  each  panel  point. 

8th.  Calculate  the  pitch  of  rivets  required  in  the  flanges 
of  the  stringers  and  floor  beams  and  the  number  of  shop  and 
field  rivets  for  their  end  connections.  (This  information  is 
frequently  given  on  the  stress  sheet.)  (21) 

9th.  Calculate  the  rivets  required  in  the  lateral  systems, 
including  portals,  to  take  the  longitudinal  and  transverse  com- 
ponents of  the  stresses  as  required. 

"While  performing  the  above  preliminary  work,  a  few 
sketches  will  be  necessary,  and  it  is  important  to  decide  upon 
the  form  of  the  connections  for  the  lower  lateral  system,  allow- 
ing clearances  for  eyebar  heads,  and  to  see  that  the  steel  work 
will  fit  the  masonry,  allowing  sufficient  clearance  at  the  ends  for 
expansion. 

No  rigid  rule  can  be  laid  down  for  the  best  order  in  which 
the  different  parts  should  be  drawn  up,  but  for  this  class  of 
structure  the  following  will  work  out  satisfactorily: 

The  scale  for  the  center  line  diagram  is  usually  %  inch,  % 
inch  or  %  inch  per  foot,  and  for  the  details,  %  inch,  1  inch, 
1^4  inch  or  1%  inch  per  foot.  The  1  inch  scale  is  used  more 
than  any  other  one  for  details. 

1st.  Draw  the  portal,  especially  if  it  is  a  skew  bridge.  A 
layout  of  the  hip  joint  will  be  necessary. 

2nd.  Work  out  the  hip  joint  with  portal  connection,  lat- 
eral connection,  pin  plates,  etc. 

3rd.  Work  out  the  shoe  joint  with  rollers,  anchor  bolts, 
masonry  plates,  shoes,,  end  strut  or  beam  and  lateral  connections, 
pin  plates,  etc. 


64  ORDER  OF  PROCEDURE.  Art.  28. 

4th.  Work  up  the  spacing  of  the  lattice  bars,  batten  plates 
and  rivets  in  the  end  posts. 

5th.  Work  up  the  lower  chord  joints,  with  floor  beam  con- 
nections, beginning  at  the  middle  of  the  truss  and  working  to- 
ward the  end. 

6th.     Finish  the  hip  vertical. 

7th.  Draw  the  top  chord  joints,  and  fix  spacing  for  lattice 
bars,  batten  plates  and  rivets  in  top  chords. 

8th.     Finish  the  intermediate  posts. 

9th.     Finish  the  top  view  of  top  chords. 

10th.  Draw  top  lateral  system  and  top  struts. 

llth.  Draw  bottom  lateral  system  and  end  struts. 

12th.  Draw  stringers  and  beams. 

13th.  See  that  each  drawing  has  a  proper  title  and  number, 
and  that  all  general  notes  required  are  on  the  drawings. 

14th.  Go  over  each  drawing  to  see  that  all  information 
which  may  be  wanted  by  the  following  persons,  is  given:  The 
checker,  the  templet  maker,  the  layer-out,  the  fitter-up,  the  in- 
spector, the  shipper,  and  the  erector.  See  that  each  piece  is 
properly  marked  and  the  number  wanted  is  given,  that  the  sizes 
of  rivets  and  open  holes  are  all  given. 

15th.  Make  a  marking  or  erection  diagram  (single  line) 
and  a  diagram  showing  how  the  bridge  is  to  be  located  on  the 
masonry. 

16th.  After  the  drawings  are  checked,  look  into  all  correc- 
tions carefully  before  doing  any  erasing.  Do  not  erase  tJie 
checker's  marks.  In  case  you  do  not  understand  the  checker's 
changes  or  see  any  reason  for  them,  ask  him  for  information. 
The  important  thing  is  to  have  the  drawing  clear  and  correct. 

Riveted  truss  'bridges  can  be  handled  in  much  the  same  way 
as  pin  connected  bridges.  The  scale  for  the  truss  drawing  is 
usually  somewhat  smaller  than  for  the  details.  Great  care  should 
be  exercised  in  order  that  connections  may  be  as  free  from  eccen- 
tricity and  as  compact  as  possible.  (12)  It  is  important  to  so 
space  rivets  that  the  net  section  of  any  member  will  not  be  less 
than  was  contemplated  in  the  design.  (11)  WTien  a  connec- 
tion is  too  complicated  to  exactly  proportion  the  rivets,  assump- 
tions should  be  made  which  will  be  on  the  safe  side. 


Art. 


PROCEDURE  FOB  PLATE  GIRDER  BRIDGE. 


66 


29.       Order   of    Procedure   for    a    Plate   Girder   Bridge. 

The  method  of  procedure  for  a  plate  girder  bridge  may  be 
outlined  as  follows:  The  scale  of  the  drawing  of  the  girder 
should  be  %  inch,  1  inch  or  l1/^  inch  per  foot.  Two  or  more 
sheets  may  be  used  for  long  girders.  For  a  skew  bridge  the  full 
length  of  one  girder  must  be  drawn.  The  girder  should  be 
drawn  first,  but  it  will  be  necessary  to  sketch  the  lateral  and 
beam  connections  before  it  can  be  completed.  The  first  thing  to 
be  considered  is  the  location  of  the  splices  in  the  web.  The  hand 
books  give  the  maximum  lengths  obtainable  for  plates  of  differ- 
ent widths  and  thicknesses.  Web  plates  up  to  about  96  inches 
wide  may  be  obtained  longer  than  convenient  for  handling  in 
the  shop.  Their  length  should  be  limited  to  from  20  to  25  feet, 
except  for  girders  less  than  30  feet  long  whose  webs  may  be 
made  without  a  splice. 


psgS  ' 

v 

^o^H 

Ch 

®rT>    V 

v 

©       (D 

1 

®  Vv    ®    /rv 

£ 
( 
£ 
£ 

i 
) 
j 

) 

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Fig.  26. 


Fig.  27. 


The  pitch  of  the  rivets  in  the  flanges  should  be  determined 
and  regular  groups  of  spacing  be  decided  on,  -as  for  example, 
2^4  inch,  2y2  inch,  3  inch,  4%  inch  and  6  inch.  Now  the  splices 
may  be  located.  If  it  is  a  deck  girder,  they  should  be  so  located 
that  there  will  be  no  odd  spaces,  if  possible,  in  the  groups  de- 
cided on.  Stiffen ers  are  always  placed  on  the  splice  plates.  The 
intermediate  stiffeners  need  not  be  spaced  so  exactly  equal  but 
that  they  may  come  on  one  of  the  rivets  previously  located,  ex- 
cept where  the  pitch  in  the  flanges  is  less  than  3  inches,  in  which 
case  a  space  of  at  least  3  inches  will  generally  be  required  on 
each  side  of  the  stiffener.  If  the  girder  is  for  a  through  bridge, 
the  splices  will  usually  be  locaited  -at  the  panel  points,  from 
which  everything  else  must  be  located.  Through  girders  often 
bave  their  top  flanges  bent  to  a  quadrant  at  the  upper  corners, 


66         PBOCEDUBE  FOB  PLATE  GIRDER  BRIDGE          Art.  29. 

and  extend  down  the  ends  of  the  girder.  This  necessitates 
splices  in  the  top  flange  near  the  bend  so  that  long  pieces  will 
not  have  to  be  bent.  All  splices  in  a  flange  should  break  joints. 

In  general  no  countersinking  is  allowed  in  girders  except  in 
the  shoe  plates.  When  the  rivets  in  the  horizontal  leg  of  a  flange 
angle  stagger  with  those  in  the  vertical  leg,  some  of  the  former 
will  interfere  with  the  outstanding  legs  of  the  stiffeners.  To 
avoid  this,  special  spacing  may  be  introduced  near  the  stiffener 
or  the  stiffeners  notched  as  shown  in  Fig.  26.  In  unusual  cases 
it  may  also  be  desirable  to  notch  the  other  leg  of  the  stiffener 
to  clear  a  rivet. 

The  horizontal  legs  of  the  flange  angles  are  usually  as  wide 
or  wider  than  the  vertical  legs.  When  the  vertical  leg  is  5  inches 
or  over,  two  rows  of  rivets  are  used  in  it.  The  practice  with 
regtard  to  the  horizontal  leg  differs.  The  simplest  way  is  to  have 
also  two  lines  of  rivets  in  each  horizontal  leg,  putting  those  of 
•the  inner  row  in  one  leg  opposite  those  of  the  outer  row  in  the 
other  leg.  This,  however,  gives  more  rivets  than  necessary 
through  the  flange  plates.  If  only  one  row  of  rivets  is  used  in 
each  horizontal  leg,  they  should  stagger  with  those  in  the  vertical 
legs.  If  two  rows  are  used  in  each  leg  the  spacing  in  the  hori- 
zontal legs  may  be  increased  to  one  and  one  half  or  two  times 
that  in  the  vertical  leg.  For  example,  where  the  spacing  in  the 
vertical  leg  is  2%  inches,  3  inches  and  4%  inches,  that  in  the 
(horizontal  legs  might  be  4%  inches,  4%  inches  and  6  inches,  or 
4%  inches,  6  inches  and  6  inches.  When  the  spacing  in  one  leg 
is  3  inches,  for  instance,  and  that  in  the  other  is  4%  inches,  the 
rivets  on  the  inner  row  of  the  4%  inch  spacing  will  stagger  with 
those  in  the  other  leg,  while  those  in  the  outer-  row  will  come 
opposite.  Three  lines  of  rivets  are  sometimes  used  in  7  inch 
and  8  inch  legs  of  angles. 

The  minimum  pitch  (7)  of  rivets  depends  upon  the  distance 
between  rivet  lines  and  the  gage  of  the  latter,  and  is  influenced 
by  clearance  for  the  riveting  tool.  In  Fig.  27  "g"  depends  upon 
the  thickness  of  the  angle.  For  large  angles,  therefore,  there 
are  usually  two  standard  gages.  In  crimped  stiffeners  the  dis- 
tance "a"  Fig.  28  should  not  be  less  than  2  inches.  Stiffeners 
should  be  placed  with  the  backs  of  the  angles  toward  the  ends 
of  the  girder.  Flange  rivets  should  not  be  located  closer  to 


Art.  29.          PROCEDURE  FOR  PLATE  GIRDER  BRIDGE. 


stiffeners  than  shown  in  Fig.  29.  This  allows  room  enough  for 
the  regular  die  of  the  riveting  machine. 

Even  if  fillers  are  not  required  under  stiffeners,  it  is  best 
to  use  them  at  points  where  beams  or  frames  connect  and  at  the 
splice  plates.  Connections  for  beams  and  frames  should,  if  pos- 
sible, be  made  in  such  a  manner  that  they  may  be  swung  into 
position  without  striking  the  rivet  heads  in  the  flanges  of  the 
girders. 

For  girder  bridges  on  a  grade,  the  girders  should,  if  pos- 
sible, be  made  so  that  they  will  fit  if  turned  end  for  end.  The 
bevel  should  be  in  the  masonry  plates  and  not  in  the  shoe  plates. 


Fig.  28. 


Fig.  29. 


30.  Shop  Bills.  Shop  bills  -acre  lists  of  material  for  use 
in  the  shop.  They  are  made  on  sheets  8%xll  inches  or  8i/2x14 
inches.  The  forms  used  by  different  companies  differ  somewhat, 
but  the  essential  features  are  as  follows : 

They  should  be  numbered  consecutively,  and  should  show 
the  number  of  the  drawing  to  which  they  refer.  Each  finished 
piece  should  be  billed  separately,  and  the  number  to  be  Chipped 
should  appear  in  the  first  column.  In  the  second  column  should 
be  given  the  number  of  constituent  parts  required  to  make  the 
number  of  .members  shown  in  the  first  column.  The  main  parts 
of  members  should  be  given  first,  the  details  following,  putting 
the  lacing  last.  Stoop  rivets  are  not  billed. 

The  size  of  each  part,  the  name  or  location,  or  both,  and  its 
length,  must  be  given.  Both  the  finished  length  and  the  ordered 
length  should  be  given  in  separate  columns.  In  the  "remarks" 
column  it  is  usually  indicated  whether  or  not  a  piece  is  to  come 
from  the  mill  or  from  stock.  Blacksmith  work,  machine  work, 
and  riveted  work  tare  usually  put  on  separate  bills.  Blank  forms 
are  sometimes  used  for  pins,  bars,  field  rivets,  etc.  Be  sure  that 
nothing  is  omitted,  as  it  might  seriously  delay  erection. 


SHOP  BILLS. 


Art.  30. 


A  check  list  for  various  kinds  of  structures  should  be  pre- 
pared, giving  all  possible  items  to  ship,  similar  to  the  ' '  Order  of 
Estimating"  given  in  Art.  19.  By  consulting  these,  omissions 
may  be  avoided. 

It  is  usually  required  to  send  drawings  to  the  shop  or  to 
have  them  printed  for  approval,  as  soon  as  they  are  finished.  If 
they  are  sent  for  approval  it  may  be  better  and  more  convenient 
not  to  make  the  bills  until  the  prints  are  returned  approved, 
as  there  may  be  some  changes.  Five  or  six  sets  of  prints  are 
required  for  the  shop.  Sending  out  drawings  before  all  parts 
of  the  structure  are  drawn  up  is  not  the  most  logical  thing  to 
do,  but  is  often  necessary. 


THE  OHIO  STATE   BRIDGE  COMPANY 


Drawing 


"lec 


/-<*** 


IS. 


Sot  1* 


ML. 


Af.L 


fiafcr/n 


2 


«.£ 


Fig.  30. 

A  simple  form  of  shop  bill  is  shown  in  Fig.  30.     The  fol- 
lowing information  should  also  be  put  on  a  bill  sheet  and  sent 
the  shop  bills : 

Contract  No.  Ship  to 

Description  Shop  Paint 

Location  Field  Paint 

Date  to  Ship  Lumber  furnished  by 

Inspected  by  Penalty 

Erected  by 


Art.  31.  SHIPMENT.  69 

In  general,  the  drawings  should  show  everything  complete, 
but  the  drawings  of  the  forge  work,  machine  shop  work,  and 
miscellaneous  details  -are  often  made  on  bill  sheets. 

31.  Shipment.  Field  splices  and  connections  are  often 
determined  by  the  limitations  of  transportation  facilities.  These 
should  be  determined  <at  the  outset.  Some  routes  can  take  eare 
of  pieces  of  greater  extreme  dimensions  than  others.  Tunnels 
often  limit  the  width  of  the  loading  and  overhead  bridges,  the 
height.  Sharp  curves  have  an  important  bearing  on  loading 
long  pieces,  especially  girders.  It  should  be  remembered  that 
a  piece  extending  over  two  or  moire  oars,  swings  away  from  the 
center  line  of  the  track  on  a  curve,  requiring  more  clearance 
than  on  a  straight  track,  and  that  a  cair  on  a  curve  is  inclined 
toward  the  inside  of  the  curve.  Ordinarily,  pieces  about  10  feet 
high  can  be  transported  on  the  railroads,  but  the  width  at  the 
top  is  usually  limited  to  -about  6  feet.  The  greatest  width  of  a 
steel  car  is  10  feet  2  inches.  Pieces  10  feet  or  more  in  width 
can  be  transported  if  they  are  not  too  high  or  too  long.  The 
question  of  weight  is  not  (generally  an  important  one,  except  that 
cars  of  proper  capacity  must  be  used  so  that  no  truck  will  be 
overloaded.  It  is  allowable  to  put  two-thirds  of  the  nominal 
capacity  of  a  car  on  one  truck. 

For  export  shipment  special  instruction  must  be  obtained  on 
each  job  as  to  maximum  lengths,  weights,  etc.  Pieces  for  export 
work  must,  "in  some  cases,  be  so  small  that  they  can  be  trans- 
ported on  pack  'animals.  A  thorough  and  simple  system  of 
marking  is  necessary.  Instead  of  marks,  colors  are  sometimes 
used. 

The  question  of  cost  of  freight  is  sometimes  an  important 
one,  and  may  determine  the  maximum  length  of  a  piece.  If  the 
total  weight  of  a  contract  is  less  than  a  car  load,  so  far  as  cost 
of  transportation  is  concerned,  no  piece  should  be  longer  than 
a  car  length. 

There  are  two  kinds  of  freight  rates,  "ear  load"  and  "less 
than  oar  load"  (C.  L.  and  L.  C.  L.),  the  latter  being  the  higher. 
The  minimum  car  load  is  generally  30,000  Ibs. ;  the  minimum  for 
two  oars  is  40,000  Ibs. ;  and  20,000  Ibs.  is  added  for  each  addi- 
tional car.  Therefore  if  any  piece  extends  from  one  oar  over 
part  of  another,  freight  must  be  paid  on  at  least  40,000  Ibs.,  no 


70  MATERIALS.  Art.  32. 

matter  how  much  less  the  shipment  weighs.  In  case  of  a  girder 
extending  over  three  cars,  the  minimum  amount  charged  would 
be  on  60,000  Ibs. 

32.  Materials.  The  materials  used  by  the  structural  en- 
gineer are  wrought  steel,  wrought  iron,  cast  steel,  cast  iron  and 
timber.  Cast  steel  and  cast  iron  are  used  for  the  machinery  of 
draw  bridges.  Except  in  special  cases  of  columns  for  buildings, 
and  pedestals,  and  for  small  details  like  washers,  ornaments  and 
separators,  cast  iron  has  passed  out  of  use  entirely  in  structural 
work.  Cast  steel  is  sometimes  used  for  shoes  of  bridges. 

Timber  is  used  for  the  compression  members  in  combination 
bridges  and  roof  trusses,  and  for  the  floors  of  bridges. 

Wrought  Iron  is  used  for  rods  which  must  be  welded, — rods 
with  loop  eyes,  or  forked  heads.  In  the  best  classes  of  work  welds 
are  entirely  avoided.  Welds  in  steel  are  not  considered  reliable. 

The  qualities  of  the  materials  required  are  given  in  the 
specifications  governing  the  work.  We  shall  consider  structural 
steel  more  in  detail. 

At  present  three  kinds  of  steel  are  commonly  specified,  viz., 
' '  rivet  steel, "  "  soft  steel ' '  and  ' l  medium  steel. ' '  Of  these,  rivet 
steel  is  the  softest  and  medium  steel  the  hardest,  or  the  steel  of 
greatest  ultimate  strength.  "Hard  steel/'  or  steel  having  an 
ultimate  strength  greater  than  70,000  Ibs.  per  sq.  in.,  is  seldom 
used  for  bridges  or  buildings. 

There  is  at  present  a  movement  toward  the  adoption  of  a 
single  grade  of  steel  for  all  structural  purposes.1  This  would 
simplify  tfhe  steel  maker's  work,  and  no  doubt  result  in  a  more 
uniform  and  a  cheaper  product. 

The  quality  of  steel  is  determined  by  analysis  and  test. 
There  is  considerable  uniformity  in  the  requirements  of  various 
specifications.  These  may  be  enumerated  as  follows : 

Chemical  re quirements,— Percentage  of  phosphorus,  sul- 
phur, manganese,  silicon,  carbon,  copper  and  arsenic. 

Physical  requirements,— Process  of  manufacture,  uniform- 
ity, finish,  heat  treatment,  ultimate  strength,  elastic  limit,  elonga- 
tion, reduction  of  area  at.  point  of  fracture,  appearance  of  f rac- 


M3ee   Bulletin  No.   62  American  Railway  Engineering  &   Mainte- 
(nance  of  Way  Association. 


Art.  32.  MATERIALS.  71 

v 
ture,  bending,  bending  after  quenching,  pun'Ching,  drifting  of 

punched  holes,  variation  of  cross  section  and  full  sized  tests. 

Chemical  analysis  determines  the  amounts  of  the  impurities 
in  steel.  All  elements  except  iron  'and  carbon  may  be  called 
impurities.  Since  it  is  practically  impossible  to  eliminate  all 
the  .phosphorus  and  sulphur,  a  small  percentage  of  manganese 
is  considered  advantageous.  In  order  to  meet  the  physical  re- 
quirements the  manufacturer  must  limit  the  amount  of  all 
impurities,  .and  of  the  icarbon.  All  specifications,  however,  limit 
the  amount  of  phosphorus  allowed,  since  this  element  renders 
the  steel  brittle  or  ' '  cold  short ' '  while  it,  at  the  same  time,  hard- 
ens it.  Some  specifications  also  specify  maximum  allowable  per- 
centages of  sulphur,  manganese  and  silicon.  The  maximum  al- 
lowable amount  of  phosphorus  in  steel  depends  upon  its  mode 
of  manufacture.  It  is  usually  about  0.04%  for  basic  open  hearth 
steel  and  0.08%  for  acid  open  hearth  and  Bessemer  steels. 

Carbon  -has  the  greatest  influence  upon  the  ultimate  strength 
or  hardness  of  steel.  Phosphorus,  manganese  and  sulphur  make 
steel  'harder  and  also  reduce  its  ductility. 

Basic  open  hearth  steel  will,  in  general,  have  about  the  fol- 
lowing ultimate  strengths,  depending  upon  the  percentage  of 
carbon : 

55000  Ibs.  per  sq.  in.  with  0.10%  carbon. 
60000  Ibs.  per  sq.  in.  with  0.15%  carbon. 
65000  Ibs.  per  sq.  in.  with  0.20%  carbon. 
70000  Ibs.  per  sq.  in,  with  0.25%  carbon. 

The  elastic  limit  will  be  about  0.6  of  the  ultimate  tensile 
strength. 

There  is  no  rigid  line  separating  the  different  grades  of 
steel,  but  steel  having  less  thian  0.15%  carbon  is  generally  soft 
steel,  and  with  more  than  0.30%  carbon,  hard  steel,  the  inter- 
mediate grade  being  medium  steel.  These  grades  are  usually 
defined  by  their  ultimate  strength. 

Process  of  Manufacture.  Steel  is  made  by  the  Bessemer  or 
open  hearth  process.  Open  hearth  steel  is  now  used  for  all  im- 
portant bridge  and  building  work.  It  is  almost  invariably  re- 
quired when  a  regular  specification  governs  the  work. 

Bessemer  steel  is  not  so  uniform  in  quality  as  open  heartK 
steel  and  is,  therefore,  not  so  reliable  a  material.  It  is  made  in  a 


72  MATERIALS.  Art.  32. 

converter,  by  blowing  a  blast  of  air  through  molten  pig  iron 
until  the  carbon  'and  silicon  are  all  burnt  out.  Ferro-mianganese 
is  then  added  to  recarbonize  the  metal  the  required  (amount  and 
to  absorb  the  excess  of  oxygen,  which  would  make  the  steel 
"rotten."  From  the  converter  the  metal  is  poured  into  -a  ladle 
and  then  into  moulds.  Here  the  metal  is  'allowed  to  solidify, 
producing  ingots.  The  ingots  are  reheated  and  then  rolled  into 
slabs,  blooms  and  billets  of  various  sizes,  depending  upon  the 
final  form  into  which  they  are  to  be  rolled. 

Open  hearth  (Siemens-Martin)  steel  is  made  in  an  open 
hearth  furnace  and  is  of  two  kinds,  acid  and  basic.  The  use  of 
the  latter  predominates. 

Acid  steel  is  made  in  a  furnace  having  a  lining  of  a  refrac- 
tory silicious  material  which  has  an  acid  reaction.  Basic  steel 
is  made  in  a  furnace  having  a  lining  of  magnesite  or  dolomite, 
which  has  (a  basic  reaction.  The  raw  material  in  either  case  is 
pig  iron,  now  usually  charged  in  (a  molten  state.  If  the  pig  iron 
contains  larger  percentages  of  phosphorus  and  sulphur  than  -are 
allowed  in  the  steel,  these  must  be  reduced.  Since  they  have  a 
great  affinity  for  iron,  some  reagent  must  be  introduced  in  the 
molten  metal  which  has  a  greater  affinity  for  them.  For  this 
purpose  a  basic  material  must  be  used,  since  they  form  acids 
when  oxidized.  The  material  employed  is  lime  charged  in  the 
form  of  limestone.  This  cannot  be  used  in  an  acid  lined  furnace 
because  it  would  form  ,a  flux  with  the  lining.  In  the  acid  process, 
therefore,  the  percentages  of  phosphorus  and  sulphur  in  the  raw 
material  must  not  much,  exceed  what  is  allowed  in  the  finished 
product.  This  process  requires  a  better  grade  of  pig  iron  than 
the  basic  process. 

In  the  open  hearth  basic  process,  large  quantities  of  oxide  of 
iron  in  the  form  of  iron  ore  or  mill  scale,  are  charged  into  the 
furnlace,  together  with  limestone  and  molten  pig  iron.  The  lime 
which  is  formed,  combines  with  part  of  the  phosphorus  and 
sulphur,  reducing  the  percentages  of  these  to  minute  quantities, 
While  the  oxide  of  iron  serves  to  burn  out  the  carbon,  manganese 
and  silicon.  The  desired  amounts  of  carbon  and  manganese  are 
then  added.  As  in  the  Bessemer  process,  the  steel  is  made  into 
ingots,  billets  land  slabs,  and  is  finally  rolled  into  the  desired 


Art.  32.  MATERIALS.  73 

Upon  the  care  with  which  all  of  these  processes  are  carried 
out  depends  the  uniformity  and  finish  of  the  rolled  steel,  as  well 
as  its  quality  to  some  extent.  Lack  of  uniformity  may  be  due  to 
unequal  heat  treatment,  unequal  working  or  to  segregation  in  the 
ingot,  producing  a  steel  of  variable  composition.  If  a  piece  of 
steel  is  not  uniformly  treated  and  cooled  there  may  be  internal 
stresses  in  it,  hence  it  is  required  that  pieces  which  are  heated  in 
working  as  eye  bars,  for  example,  must  be  annealed.  The  hotter 
a  piece  of  steel  is  heated,  the  coarser  grained  it  will  be  and  the 
more  rapidly  it  is  cooled,  the  harder  it  will  be.  Rolling  and  ham- 
mering steel  increases  its  density  and  strength,  -but  working  it 
at  a  blue  heat  may  crush  the  grain,  which  is  very  injurious. 
Hough  iron  cracks  are  indications  of  ' '  red  shortness ' '  or  burning. 
Other  surface  defects  are  easily  discovered  on  close  inspection. 
Defects  due  to  bad  heat  treatment,  improper  working,  excess  of 
impurities,  etc.,  are  discovered  by  chemical  analysis  and  physical 
tests.  Tests  are  made  of  material  from  e&ch  heat,  melt  or  blow. 

Specifications  allow  a  range  of  8,000  to  10,000  Ibs.  per  sq. 
in.  in  the  ultimate  tensile  strength  of  any  particular  grade  of 
steel,  but  they  do  not  all  agree  as  to  the  limits.  Depending  upon 
the  specifications,  soft  steel  miay  include  steel  having  an  ultimate 
strength  as  low  as  52,000  Ibs.  per  sq.  in.  and  as  high  as  62,000 
Ibs.  per  sq.  in.,  medium  steel  as  low  as  60,000  and  'as  high  as 
70,000  Ibs.  per  sq.  in.,  and  rivet  steed  from  48,000  to  58,000  Ibs. 
per  sq.  in. 

The  ultimate  strength,  elastic  limit,  elongation  and  reduc- 
tion of  area  are  determined  from  test  pieces  cut  from  the  finished 
material.  It  is  usually  required  that  the  elastic  limit  must  not 
be  less  than  one  half  of  the  ultimate  strength.  As  it  is  not  diffi- 
cult to  obtain  an  elastic  limit  equal  to  0.6  of  the  ultimate  strength 
it  would  be  well  to  specify,  as  is  sometimes  done,  a  minimum  for 
the  elastic  limit.  Thus,  if  the  ultinuate  may  vary  from  60,000  to 
68,000  Ibs.  per  sq.  in.,  the  minimum  elastic  limit  might  be  fixed 
at  32,000  Ibs.,  for  example,  and  then  steel  having  a  greater  ulti- 
mate than  64,000  Ibs.,  would  hav-Q  to  have  an  elastic  limit  of  at 
least  one  half  the  ultimlate.  In  this  case  the  unit  stresses  could 
be  based  upon  an  elastic  limit  of  32,000  Ibs. 


74  MATERIALS.  Art.  32. 

In  commercial  testing,  the  elastic  limit  is  determined  by  the 
drop  of  the  beam  of  the  testing  machine,  that  is,  it  is  really  the 
yield  point.1 

It  is  important  thiat  steel  be  ductile  and  not  brittle.  For 
determining  ductility,  the  tension  piece  is  measured  after  rup- 
ture to  determine  the  stretch  in  an  original  length  of  eight 
inches,  and  the  reduction  of  area  at  the  point  of  fracture.  The 
determination  of  the  latter  is  not  important  and  is  usually 
omitted.  In  a  general  way,  the  elongation  in  eight  inches  is 
about  30%  for  good  steel  having  an  ultimate  strength  of  56,000 
Ibs.  per  sq.  in.,  and  25%  for  65,000  Ib.  steel.  This  is  for  standard 
test  specimens  having  an  area  of  cross  section  of  not  less  than 
y2  sq.  in.  The  usual  requirements  are  25%  for  soft  steel  and 
22%  for  medium.  Pin  material  is  only  required  to  have  an 
elongation  of  16%  or  17%,  and  eye  bars,  when  tested  full  size, 
10%  in  the  body  of  the  bar. 

The  percentage  of  reduction  of  area  is  about  1.8  to  1.9  times 
that  of  the  elongation. 

The  appearance  of  the  surface  of  the  fracture  is  always 
noted  in  testing  steel.  If  it  shows  defects  such  -as  blisters,  cin- 
ders, spots,  cracks  or  laick  of  uniformity  of  color,  it  is  not  a 
desirable  product.  The  fracture  of  good  material  is  described 
as  " silky, "  and  has  a  "uniform,  fine  grained,  structure  of  blue 
steel  gray  color,  entirely  free  from  fiery  l luster'  or  a  'blackish' 
cast."  If  the  fracture  is  granular  and  has  a  ' fiery"  lutser  it 
indicates  over  heating.  If  the  fracture  is  dull  or  "sandy,"  the 
steel  is  impure,  or  worked  cold,  and  sfliould  be  rejected. 

The  bending  test  requires  that  the  test  piece  shall  bend  cold 
without  sign  of  fracture.  For  soft  steel  it  must  bend  flat  on 
itself,  and  for  medium  steel,  to  a  curve  whose  diameter  is  from 
one  to  three  times  the  thickness  of  the  piece  tested.  Some  speci- 
fications require  this  bending  test  to  be  miade  upon  pieces  which 
have  been  heated  and  quenched  in  water, 

A  punching  test  is  sometimes  specified.  This  requires  that 
the  walls  between  the  punched  holes  shall  not  break  down  except 
Mien  they  are  less  than  %  inch  thick. 


JSee  Heller's  "Stresses  in  Structures,"  Art.  21. 


Art.  33.  INSPECTION.  75 

The  drifting  Ust  requires  that  the  ductility  of  the  metal 
must  be  such  that  a  punched  hole  will  stand  drifting  until  its 
diameter  is  increased  from  33%  to  100%  without  cracking  the 


Pieces  of  large  cross  section  are  apt  to  be  "piped,"  that 
is,  they  are  not  solid.  This  is  due  to  bad  working  or  unequal 
cooling,  and  occurs  particularly  in  pins.  It  is  usually  specified 
that  the  larger  sizes  of  pins  (say  over  4%  inches)  must  be  forged 
from  blooms  having  a  sectional  area  of  about  three  times  the 
area  of  the  pin,  in  order  that  the  material  may  be  sufficiently 
worked  to  make  it  sound. 

Full  sized  tests  are  usually  confined  to  eye  bars.  Some  re- 
ductions in  requirements  of  ultimate  strength  and  elongation 
are  made  from  those  required  for  small  test  pieces,  because 
pieces  of  large  cross  section  do  not  test  as  high  as  those  of  small 
cross  section. 

33.  Inspection.  If  an  inspector  is  employed  on  a  con- 
tract, his  duties  may  relate  to  material,  shop  work  and  erection. 
On  some  classes  of  work  the  purchaser  employs  no  inspector. 
The  manufacturer  has  all  work  inspected  as  to  dimensions,  to 
avoid  trouble  in  erection.  In  some  cases  reports  of  tests  of 
material  are  furnished  by  the  rolling  mill,  which  conducts  a  test- 
ing department  for  this  and  other  purposes. 

An  inspector  is  most  frequently  employed  to  make  tests  of 
the  steel,  at  the  mill,  as  it  is  rolled.  The  shop  work  is  also 
inspected  for  the  best  classes  of  work,  but  in  comparatively  few 
cases  is  the  field  work  inspected  by  a  regular  inspector.  The 
large  railway  companies  have  inspectors  in  the  mills,  the  shop, 
and  the  field. 

The  inspection  of  material  includes  tests,  analyses,  surface 
inspection,  measuring  sizes,  etc.,  of  steel,  lumber,  paint,  etc.  A 
shop  inspector  should  see  that  no  material  is  injuriously  treated, 
that  reaming  of  rivet  holes  is  properly  done,  that  all  parts  are 
made  in  accordance  with  the  drawings,  that  rivets  are  good  and 
tight,  that  members  are  straight,  that  no  work  is  ragged  or  un- 
finished, that  painting  is  done  in  accordance  with  the  specifica- 
tions, and  should  make  reports  of  progress. 


76  INSPECTION.  Art.  33. 

The  field  inspector  should  see  that  no  part  of  the  structure 
is  injuriously  treated,  that  no  members  are  interchanged,  that  all 
field  driven  rivets  are  good,  and  that  the  painting  is  properly 
done. 

Hare  qualifications  are  required  for  a  good  inspector.  He 
must  serve  his  employer  honestly  and  avoid  friction  with  the 
contractor. 


CHAPTER  IV. 
ROOFS. 

The  roofs  of  buildings  in  which  it  is  not  desirable  to  have 
columns  at  frequent  intervals,  are  supported  by  means  of  trusses 
Which  are  in  turn  carried  either  on  columns  at  the  sides  or  on 
masonry  walls.  These  trusses  may  be  either  of  steel  or  a  com- 
bination of  wood  and  steel.  Steel  trusses  are  usually  used  in 
steel  or  brick,  mill  and  factory  buildings,  and  in  fire  proof 
buildings.  Combination  trusses  are  used  in  wooden  buildings 
requiring  a  large  floor  space  free  from  columns,  and  often  also 
in  large  brick  and  stone  buildings,  such  as  churches  and  public 
buildings  of  all  kinds. 

34.  Construction.      The   roof  trusses   are  placed  trans- 
versely of  the  building,  their  distance  apart  (See  Art.  37)  de- 
pending on  the  length  of  span,  type  of  construction  of  the 
building  in  general  and  the  kind  of  roof  covering.     The  upper 
inclined  members  of  the  trusses,  parallel  to  the  slope  of  the  roof 
are  called  rafters.     (See  Fig.  31.)     Longitudinal  beams  extend- 
ing from  truss  to  truss  are  supported  by  the  trusses  at  intervals 
along  the  rafters.     These  are  purlins,  and  they  carry  the  roof 
covering,  either  directly  or  by  means  of  boards,  called  sheeting 
or  sheathing,  running  transversely  to  the  purlins  (up  and  down 
the  roof)  or  diagonally  across  them. 

35.  Roof  Coverings.     For  mill  buildings,  the  commonest 
kinds  of  roofing  are  corrugated  steel  or  iron,  slate,  tile,  tin  and 
various  patent  sheet  metal  roofs,  tar  and  gravel  and  similar 
patented  combinations. 

The  corrugated  steel  or  iron  is  usually  fastened  directly  to 
the  purlins  by  means  of  clips.1  Slate  is  usually  nailed  to  sheet- 
ing boards  with  -a  layer  of  roofing  felt  between,  although  some- 
times heavy  slate  is  fastened  directly  to  small  purlins  placed 
about  10%  inches  apart.  Tile  is  usually  fastened  directly  to 


'See  "General  Specifications  for  Steel  Roofs  and  Buildings,"  by 
C.  B.  Fowler,  Figures  page  17. 


78  TYPES  OF  TRUSSES.  Art.  36. 

angle  purlins  spaced  about  13  inches  apart,  without  any  sheet- 
ing. Tin,  and  similar  types  of  roofing  are  laid  on  sheeting  with 
roofing  felt  between.  Tar  and  gravel  roofs  are  laid  on  woodeu 
sheeting  or  sometimes  on  reinforced  concrete  slabs. 

The  main  function  of  the  roof  is  to  shed  water,  and  in  order 
to  do  this  without  leakage,  it  must  have  a  fall  or  slope.  The 
amount  of  slope  required  depends  upon  the  kind  of  roof 
covering. 

T>he  pitch  of  a  roof  is  the  ratio  of  its  rise  to  its  span.  Thus 
for  a  60  ft.  span,  if  the  rise  is  15  ft.,  the  pitch  is  %,  if  the  rise 
is  20  ft.  the  pitch  is  %.  The  least  pitch  advisable  to  use  with 
corrugated  steel  slate  or  tile  is  about  %,  that  is  a  fall  of  about 
6  inches  per  foot,  and  this  is  the  pitch  used  for  most  mill  and 
factory  buildings.  Tin  'and  similar  roofs  with  water  tight  joints 
may  have  a  fall  of  as  little  as  %  inch  per  foot.  Tar  and  gravel 
roofs  should  have  a  fall  of  from  %  in.  to  2  in.  per  foot. 

36.  Types  of  Trusses.  It  is  only  in  unusual  structures 
such  as  train  sheds,  exposition  buildings,  grand  stands,  etc., 
that  the  span  of  a  roof  truss  exceeds  100  ft.  The  slope  of  the 
roof  and  local  conditions  such  -as  required  clearances,  ventila- 
tion, light,  etc.,  will  usually  determine  the  general  outline  of  the 
truss.  Any  type  of  bracing  may  then  be  selected  to  suit  the 
materials  of  construction.1 

For  roofs  of  ordinary  pitch  and  span,  the  Fink  truss  is  by 
far  the  commonest  type.  Figure  31  (a),  (b),  (c)  and  (d)  shows 
several  modifications  of  this  form  of  truss,  to  suit  spans  of  vary- 
ing length.  For  sake  of  economy  in  the  rafters  it  is  not  desirable 
to  have  many  loads  coming  on  them  from  the  roof  purlins,  be- 
tween panel  points,  hence  the  advisability  of  increasing  the 
number  of  panels  <as  the  span  increases. 

For  combination  trusses  of  wood  and  iron,  one  of  the  forms 
shown  in  Fig.  31  (g)  and  (h)  is  used.  In  these  trusses  the 
diagonal  compression  members  and  the  top  und  bottom  chords 
are  made  of  wood,  and  the  vertical  ties  are  rods. 

For  flat  roofs  some  form  of  truss  must  be  used  similar  to 
Fig.  31  (f),  (h)  <and  (1),  in  order  to  gain  sufficient  depth  at  the 
center  to  give  economic  chord  sections. 

JSee  Heller's  "Stresses  in  .Structures,"  Art.  117. 
See  Ketchum's  ''Steel  Mill  Buildings,"  page  146. 


Art.  86. 


TYPES  OF  TRUSSES. 


79 


Another  type  of  roof  wlhiclh  is  rapidly  coming  into  favor  is 
the  "saw-tooth"  roof,  shown  in  Fig.  31  (k).  The  plane  of  the 
steeper  rafter  is  glazed,  and  this  side  is  made  to  face  the  North 
if  possible.  By  this  arrangement  the  floor  below  is  lighted  by 
an  even  diffused  light,  without  the  necessity  of  making  the 
building  narrow  in  order  to  gain  ligfht  from  the  sides,  and  with- 
out the  disadvantages  of  sky  lights  through,  which  the  direct 
rays  of  the  sun  may  shine. 

Roof  trusses  for  very  long  spans  are  usually  three-hinged 
arches,  the  lower  hinges  being  connected  by  bars  under  the  floor 
to  take  the  tfhrust.1 


Fig.  31. 


The  roof  trusses  of  grandstands  usually  project  beyond 
their  supports  at  both  ends.  These  are  called  cantilever  trusses. 

Sometimes  for  the  sake  of  appearance  or  to  gain  clearance, 
the  lower  chord  of  a  roof  truss  is  curved  upward.  This  always 
increases  the  cost  and  weight  very  materially. 


JSee  trainsheds  for  Penna.  R.  R.  at  Jersey  City  and  Philadelphia, 
and  of  the  Phila.  and  Reading  R.  R.  at  Philadelphia,  in  Eng.  News,  Vol. 
26,  p.  276  and  Vol.  29,  pp.  507  and  508,  Vol.  42,  p.  212. 


80  BUILDING  CONSTRUCTION.  Art.  37. 

Ordinary  roof  trusses  are  made  with  riveted  connections, 
because  such  construction  is  cheaper  and  gives  greater  rigidity 
than  the  pin  connection.  Heavy  trusses  of  long  span  are  some- 
times made  with  pin  connections,  because  the  saving  in  cost  of 
erection  is  more  than  the  slaving  in  shop  work  with  riveted  con- 
nections. The  members  of  a  pin  connected  truss  offer  a  smaller 
percentage  of  area  to  the  corrosive  action  of  gases  than  those 
of  riveted  trusses.  Provision  is  sometimes  made  for  the  weaken- 
ing effect  of  corrosion,  by  increasing  the  thickness  of  material 
above  that  required  to  take  the  actual  stresses  or  by  adding  a 
certain  percentage  to  the  loads.1 

In  calculating  the  relative  economy  of  roofs  of  different 
pitches,  the  roof  covering  must  be  taken  into  account,  as  the 
greater  the  pitch,  the  greater  the  area  of  roof  covering.  Corru- 
gated steel  usually  makes  the  cheapest  roof,  as  the  dead  weight 
is  small.  The  most  expensive  roofs  are  those  of  tile  and  heavy 
slate,  laid  directly  on  the  purlins. 

37.  Building  Construction.  Trusses  carrying  light  roofs 
are  usually  spaced  from  16  ft.  to  20  ft.  center  to  center.  Theo- 
retically the  shorter  this  spacing,  the  less  the  total  weight  of 
trusses  and  purlins,  per  sq.  ft.  of  covered  area,  but  on  account 
of  practical  limitations  in  the  size  of  materials,  etc.,2  and  on 
account  of  the  greater  cost  per  pound  for  the  manufacture  of 
trusses,  than  for  purlins,  the  spacing  of  the  heaviest  trusses  is 
very  seldom  less  than  10  ft.  center  to  center.  When  the  weight 
of  the  roof  covering  is  very  great,  the  purlins  are  sometimes 
supported  between  trusses,  on  beams  called  "jack  rafters," 
which  are  supported  at  the  ridge  -and  eave,  on  longitudinal 
beams,  carried  by  the  trusses. 

For  a  building  with  masonry  walls,  no  wind  bracing  is 
neicessary  unless  the  end  walls  do  not  run  up  to  the  roof,  "but 
some  bracing  is  usually  put  in  to  facilitate  erection  and  to 
stiffen  the  roof. 

In  steel  buildings  bracing  is  necessary  to  provide  for  both 
longitudinal  and  transverse  wind  forces,  and  to  stiffen  the  build- 
ing in  case  there  is  any  vibration  due  to  live  loads,  shafting  or 
machinery. 

i"See  Fowler's  Specifications  for  Steel  Roofs  and  Buildings,  Art.  10. 
2See  Fowler's  Spec.  Arts.  37,  39,  44,  45,  59,  and  64. 


Art.  37.  BUILDING  CONSTRUCTION.  81 

With  the  ordinary  Fink  truss,  the  transverse  bracing  con- 
sists of  knee  braces  connecting 
the  trusses  and  columns,  as 
shown  in  Fig.  32,  the  wind  load 
being  carried  to  the  founda- 
tions by  bending  in  the  columns. 
If  a  truss  is  used  having  some 
depth  at  the  ends,  (see  Fig.  31 
(f),  (h),  (1),)  the  knee  braces 
may  be  dispensed  with  and  the 
columns  run  through  to  the  rafter.1 

Longitudinal  bracing  may  be  put  in,  in  three  planes.  That 
in  the  plane  of  the  rafters  is  called  rafter  bracing,  that  in  the 
plane  of  the  bottom  chords  is  called  bottom  chord  bracing,  and 
that  in  the  vertical  planes  between  the  columns  is  called  side 
bracing. 

Theoretically,  only  one  panel  of  longitudinal  bracing  is 
necessary  to  take  care  of  the  longitudinal  wind  forces,  but  for 
convenience  in  erecting  the  steel  work,  not  less  than  two  panels 
are  braced,  and  in  long  buildings  the  braced  panels  are  not 
farther  apart  than  three  or  four  panels.  This  arrangement  us- 
ually requires  less  material  in  the  bottom  chord  and  rafter 
bracing  diagonals  than  is  given  by  the  smallest  size  of  rod  ever 
used,  and  these  members  are  therefore  usually  made  of  %  inch 
round  rods.  Struts  are  required  between  the  trusses  and  col- 
umns as  members  of  the  lateral  systems.  In  the  rafter  bracing, 
the  roof  purlins  are  usually  made  to  serve  the  purpose  of  struts. 
Several  lines  of  ties  are  put  between  the  bottom  chords  of  the 
trusses  in  the  unbraced  panels.  These  serve  to  reduce  the  vibra- 
tion of  the  roof,  especially  when  cranes  or  hoists  are  attached  to 
the  trusses.  The  general  arrangement  of  the  bracing  is  shown 
in  the  stress  sheet,  Fig.  35. 

38.  Loads.  A  roof  truss  ordinarily  carries  nothing  but 
dead  loads,  which  includes  wind  and  snow  loads  and  the  weight 
of  the  structure  itself,  such  'as  the  covering,  sheeting,  purlins, 
trusses,  bracing,  ceiling,  shafting,  etc.  A  traveling  hoist  carried 
by  a  roof  truss  would  constitute  a  live  load. 


aFor  figuring  stresses  in  Columns  see  Heller's  "Stresses  in  Struc- 
tures," Chap.  X  and  XIV. 


82  LOADS.  Art.  38. 

The  pressure  of  a  gas  or  liquid  is  always  normal  to  the 
surface  on  which  it  acts,  consequently  the  wind  load  acts  nor- 
mally to  the  surface  of  the  roof.  All  other  loads  act  vertically, 
and  are  estimated  in  pounds  per  horizontal  square  foot.  The 
wind  is  assumed  to  blow  horizontally,  the  pressure  which  it 
exerts  depending  upon  its  velocity.  An  empirical  formula  fre- 
quently used  is  W=0.004F2  in  which  W  is  pressure  per  sq.  ft. 
in  pounds,  on  a  surface  perpendicular  to  the  direction  of  the 
wind,  and  V  is  velocity  in  miles  per  hour.  Experiments  extend- 
ing over  seven  years  at  the  site  of  the  Forth  bridge  in  Scotland, 
show  that  the  pressure  on  large  surfaces  is  much  less  per  sq.  ft. 
than  on  small  ones.  The  maximum  pressure  recorded  on  a 
surface  of  l^  sq.  ft.,  was  41  Ibs.  per  sq.  ft.,  and  on  a  surface 
of  300  sq.  ft.,  was  only  27  Ibs.  per  sq.  ft. 

The  roof  of  a  building  presents  a  large  surface,  and  is 
usually  figured  for  a  wind  load  due  to  a  horizontal  force  of  30 
Ibs.  per  sq.  ft.  The  sides  and  ends  of  buildings  are  usually 
figured  for  ia  miaximum  wind  pressure  of  from  20  to  30  Ibs.  per 
sq.  ft.,  but  this  pressure  is  often  taken  as  low  as  10  Ibs.  per 
sq.  ft.1 

The  normal  wind  pressures  on  roofs  of  various  pitches  for 
a  horizontal  wind  force  of  30  Ibs.  per  sq.  ft.  are  given  in  Fow- 
ler's Specifications  for  Steel  Roofs  and  Buildings,  Art.  6.  These 
are  based  on  the  empirical  formula, 

•W'=WsiWi-84c.s"-i)  in  which 

W— normal  pressure  per  sq.  ft. 

W=horizontal  pressure  per  sq.  ft. 

a    =&ngle  of  inclination  of  the  roof  with  the  horizontal. 

In  the  article  referred  to,  the  columns  marked  "Vertical" 
and  "Horizontal"  are  not  the  ordinary  components  of  the  nor- 
mal given,  but  they  do  not  differ  much  from  them. 

«,  When  a  roof  truss  rests  on  masonry  walls,  one  end  must  be 
free  to  move  longitudinally,  in  order  to  provide  for  changes  in 
length  due  to  temperature  changes.  This  is  usually  arranged 
by  providing  slotted  holes  in  one  end  for  the  anchor  bolts,  thus 
allowing  the  truss  to  slide  on  the  bed  plate.  For  long  trusses 
rollers  are  provided  to  reduce  the  friction  where  this  movement 

1See  Fowler's  Specifications,  Art.  7. 

See  "Wind  Pressures  in  the  St,  Louis  Tornado,"  by  Julius  Baier, 
in  Trans.  Am.  Soc.  C.  E.,  Vol.  37,  p.  221. 


Art.  38.  LOADS.  83 

takes  place.  If  we  assume  that  there  is  no  friction  at  the  ex- 
pansion bearing,  the  reaction  must  be  vertical  at  that  point  and 
therefore  it  is  necessary  to  calculate  the  stresses  in  the  truss 
with  the  wind  blowing  from  both  directions.  When  trusses  are 
fastened  rigidly  to  the  top  of  columns,  the  horizontal  compo- 
nents of  the  wind  reactions  are  sometimes  assumed  to  be  equal 
and  sometimes  the  wind  reactions  are  assumed  parallel.  In  the 
latter  case  it  is  only  necessary  to  calculate  the  stresses  for  the 
wind  blowing  in  one  direction.  A  vertical  equivalent  wind  load 
is  sometimes  used  together  with  the  other  loads,  as  explained 
below. 

The  snow  load  varies  with  the  climate,  the  slope  of  the  roof 
and  the  roughness  of  the  roof  covering.1  The  weight  of  freshly 
fallen  snow  is  from  5  to  12  pounds  per  cu.  ft.2  The  snow  load 
may  act  on  one  side  only  of  'a  roof,  as  a  heavy  wind  or  the  sun 
on  the  other  side  would  dislodge  it.  When  the  pitch  of  the  roof 
is  variable,  as  it  frequently  is  for  train  sheds,  snow  might  stand 
on  only  a  part  of  either  or  both  sides,  and  might  be  a  variable 
load.  It  is  not  usually  assumed  that  the  maximum  wind  and 
snow  loads  can  act  upon  one  side  of  a  roof  at  the  same  time, 
because  the  wind  would  dislodge  the  snow. 

We  may  therefore  have  a  partial  snow  load,  -a  partial  wind 
load  or  a  combination  of  these,  in  addition  to  the  weight  of  the 
structure  itself. 

For  the  ordinary  Fink  roof  truss  of  %  pitch  or  less,  none  of 
these  partial  loads  give  maximum  stresses,  and  an  equivalent 
wind  and  snow  load  is  usually  taken  as  acting  vertically  over 
the  entire  roof.  This  simplifies  the  calculation  of  stresses,  and 
is  used  whether  or  not  the  trusses  rest  on  rollers  at  one  end.3 

The  weight  of  the  roof  covering  should  be  calculated,  re- 
membering that  the  weight  per  horizontal  square  foot  is  equal 
to  the  weight  per  sq.  ft.  of  the  roof  surface  multiplied  by  the 
secant  of  the  angle  of  inclination  of  the  roof  with  the  hori- 
zontal.4 


'See  Fowler's  Specifications,  Art.  5. 
2See  Trautwine's  "Civil  Engineer's  Pocket  Book,"  p.  384. 
"See  Fowler's  Specifications,  Art.  12. 

4:For  weights  of  various  roofing  materials,  see  Trautwine's  "Civil 
Engineer's  Pocket  Book."     See  aJlso  Fowler's  Specifications.  Art.  8. 


84  LOADS.  Art.  38. 

The  thickness  of  the  sheeting  when  used  depends  upon  the 
spacing  of  the  purlins.  It  varies  from  %  in'  to  2  in.  in  thick- 
ness, and  may  be  calculated,  using  an  extreme  fiber  stress  of 
from  1200  to  1500  Ibs.  per  sq.  in.1 

The  weight  of  the  purlins  -may  be  calculated  after  they  are 
designed,  which  is  usually  done  before  the  trusses  are  figured. 
For  'Corrugated  iron  roofs  they  will  usually  amount  to  about 
3  Ibs.  per  horizontal  square  foot. 

The  weight  of  the  trusses  may  be  estimated  from  a  compari- 
son with  a  similar  building  which  has  been  designed,  or  it 
may  be  approximately  obtained  from  an  empirical  formula.2 
After  the  design  is  completed,  an  estimate  of  the  weight  is  made 
and  the  dead  load  used  in  the  calculations  is  verified.  If  this 
differs  materially  from  the  amount  used,  corrections  in  the 
design  should  be  made. 

39.  Stresses.     The  stresses  in  any  statically  determinate 
structure3  may  be  calculated  from  the  principles  of  statics.*  For 
ordinary  trusses  the  loads  and  reactions  are  all  taken  vertical. 
Since  trusses  of  the  same  type  with  the  same  number  of  panels 
are  similar  figures,  the  stresses  in  them  are  proportional,  for 
different  spans,  to  the  panel  loads.    Tables  of  stresses  in  various 
types  of  trusses  for  panel  loads  of  one  pound  are  given  in  var- 
ious hand  books.5    The  stress  in  any  member  of  a  truss  similar 
to  any  of  these  is  gotten  fay  multiplying  the  coefficient  given,  by 
the  panel  load.    This  is  readily  done  on  the  slide  rule. 

40.  The  Design  of  a  Roof.      To  illustrate  the  method  of 
procedure  we  will  now  give  a  complete  design  of  a  roof.     The 
following  data  will  be  assumed : 

The  extreme  width  out  to  out  of  pilasters  will  be  81  ft.  1  in. 

The  extreme  length  of  building  will  be  221  ft.  1  in.  This 
will  give  a  length  of  220  ft.  center  to  center  of  end  walls,  as- 
suming the  walls  to  be  13  in.  thick,  and  a  width  of  80  ft.  center 
to  center. 


iSee  Fowler's  Specifictions,  Art.  22. 
2  See  Fowler's  Specification's,  Art.  9. 
8See  Heller's  "Stresses  in  Structures,"  Art.  42. 
*See  Heller's  "Stresses  in  Structures,"  Chapters  III,  IV,  V  and  VI. 
6S«e  Fowler's  Specifications,  pages  10  to  15.    See  also    Carnegie's 
Pocketbook,  page  174. 


Art.  40.  THE  DESIGN  OF  A  HOOF.  86 

The  end  walls  will  run  up  to  the  roof  and  carry  the  end 
panel  purlins. 

We  will  use  11  bays  at  20  ft.=220  ft. 

Eoof  covering  to  be  No.  20  Corrugated  Steel. 

Specifications  to  be  Fowler's  "Specifications  for  Steel  Roofs 
and  Buildings/'  1904  edition. 

Pitch  of  the  roof  to  be  one  fourth. 

The  stress  sheet,  Fig.  35,  gives  a  general  outline  of  the 
arrangement  of  the  purlins,  bracing,  etc. 

The  student  should  familiarize  himself  with  the  specifica- 
tions and  refer  to  them  constantly. 

Loads:—  Snow   (Spec.  Art.  5)  15  Ibs.  per  horiz.  sq.  ft. 

Wind  (Spec.  Art.  6)  Vertical  15  Ibs.  per  horiz.  sq.  ft. 
Corr.  Steel  No.  20  (Spec.  Art.  8)  2  Ibs.  per  horiz.  sq.  ft. 
Purlins  say  3  Ibs.  per  horiz.  sq.  ft. 

Total  carried  by  the  Purlins        35  Ibs.  per  horiz.  sq.  ft. 

For  corrugated  steel  No.  20  the  roof  purlins  must  not  be 
spaced  over  4  ft.  6  in.  center  to  center  (Spec.  Art.  27).  The 
extreme  length  of  the  rafter  is  y  (  40.5  )2+(  20.25)  2=45.3  ft.  If 
we  use  11  purlins,  their  distance  center  to  center  will  be  almost 
exactly  4  ft.  6  in.  This  arrangement  will  not  make  the  purlins 
come  at  the  panel  points  of  the  truss  (See  Fig.  35)  but  this  can- 
not be  avoided,  hence  the  rafters  must  also  act  as  beams  to  carry 
the  purlin  loads  to  the  panel  points  of  the  truss,  as  well  as 
members  taking  the  regular  truss  stress. 

The  number  of  horizontal  square  feet  tributary  to  each 

purlin  is  —  X  20=81  sq.  ft.,  which  at  35  Ibs.  per  sq.  ft.  gives 

2835  Ibs.  total  load  on  each  purlin.     The  maximum  moment 
2835X20 


1^=85^50  in.  Ibs.      The  maxi- 

8  8  :    v^.    ' 

mum  allowed  extreme  fiber  stress  for  purlins  is  15000  Ibs.  per 
sq.  in.  (Spec.  Art.  19). 

M         I         85050       -  »„  .   ... 

—  =  —  =  —  —  -«=5.67=required  section  modulus* 
«         v       16000 

The  lightest  I  beam  with  a  section  modulus  greater  than 
5.67,  is  a  6  in.  I  x  12%  Ibs.  (See  Cambria,  page  160).  The  light- 
est channel  having  the  required  section  modulus  in  a  7  in.  chan- 


86  THE  DESIGN  OF  A  ROOF.  Art.  40. 

nel  9%  Ibs.,  the  lightest  angle  that  can  be  used  is  a  7  in.  x  3%  in. 
x  1/2  in->  which  weighs  17.0  Ibs.  per  ft.  The  I  beam  would  be 
better  than  the  channel,  because  it  is  considerably  stiffer  side- 
wise,  but  it  weighs  considerably  more.  Channels  are  usually 
used  in  such  positions  and  we  will  use  the  channel. 

The  above  method  of  calculating  purlins  is  not  correct, 
since  the  moment  of  inertia  which  we  used  in  the  calculation  is 
not  about  ;an  axis  perpendicular  to  the  plane  of  the  loads.1  It 
is,  however,  close  enough  if  the  purlins  are  held  from  deflecting 
in  the  plane  of  the  roof,  and  is  the  method  always  used.  To  pre- 
vent the  purlins  from  sagging  and  to  take  the  component  of  the 
load  parallel  to  the  roof,  sag  ties  are  inserted  at  distances  not 
more  than  about  30  times  the  width  of  the  purlin  apart.  (Spec. 
Art.  42. )  These  are  usually  made  of  %  in.  round  rods  threaded 
at  the  ends,  which  are  run  through  holes  in  the  purlin  webs  with 
nuts  to  hold  them  in  place.  They  are  carried  across  the  ridge 
in  such  a  manner  that  the  loads  on  the  two  sides  of  the  roof 
balance  each  other. 

The  purlins  are  fastened  to  the  rafters  by  means  of  angle 
clips  as  shown  in  the  truss  drawing,  Fig.  36  (Spec.  Art.  49). 
The  clip  should  be  below  the  purlin  to  facilitate  erection. 

We  can  now  make  an  estimate  of  the  weight  of  our  purlins. 

One  purlin  weighs  93/4X20=195  Ibs.  22  purlins=22Xl95 
=4290  Ibs.  per  bay.  Sag  ties=3X 2X46=276  lin.  ft.  276X1.04 
=287  Ibs.  per  bay.  About  10%  should  be  added  to  this  for  nuts 
and  laps,  making  320  Ibs.  per  bay.  Total  weight  then  is 
320+4290=4610  Ibs.  per  bay.  This  is  distributed  over  81X20 

=1620  sq.  ft.    The  weight  per  sq.  ft.  then  is  ^li=2.85  Ibs.  per 

1620 

sq.  ft.    Our  estimate  was  3  Ibs.  per  sq.  ft. 

The  weight  of  the  trusses  may  now  be  calculated  approxi- 
mately from  the  formula  given  in  Art.  9  of  the  specifications. 
0.04X80+0.4=3.6  Ibs.  per  sq.  ft.  Calling  this  4  Ibs.  we  have 
35+4=39  Ibs.  per  horiz.  sq.  ft.  for  the  truss  load.  For  the 
purlin  spacing  which  we  have,  no  two  panel  loads  on  the  truss 
will,  in  general,  be  the  same,  but  it  is  sufficiently  close  to  assume 


aFor  a  complete  discussion  of  this  subject  see  Heller's  "Stresses 
in  Structures,"  Art  69. 


Art.  40. 


THE  DESIGN  OF  A  ROOF. 


87 


them  all  equal  for  the  stresses  in  the  truss.    The  panel  load  then 
will  be  10X20X39=7800  Ibs. 

By  means  of  the  table  on  page  13  of  the  specifications,  we 
find  the  following  stresses  for  a  panel  load  of  7800  Ibs.  (Note 
that  the  lettering  of  the  truss  in  the  specifications  is  not  the 
same  as  used  here.) 


fog*. 


fbd 


tfrea 


Stress 


f 


364 
3./Z 
2.08 


f/tir.   JL 


0.89 
2*4 
OJ9 


0.6f 
035 
O.61 


S6 


/.66 
2.64 
/.8S 


0.<52 
0.S2 


JL 
JL 


/.SOW 
/J6 


/.& 


The  tension  members  may  be  proportioned  first.  The  small- 
est angle  allowed  is  2  in.  X  2  in.  X  %  in->  (Spec.  Art.  64),  and 
all  members  should  be  symmetrical  (Spec.  Art.  39  and  40). 
Therefore  the  smallest  member  allowed  will  be  2  Ls  2"X2"X1/4". 
The  largest  rivets  allowed  in  these  angles  are  %  in.  (See  Cam- 
bria, page  54).  The  gross  area  is  2X0.94=1.88  sq.  in.  The  net 
area  is  1.88-(2X1/4X(%+1/8)=1.88-0.38=1.50  sq.  in.  This 
will  answer  for  6C,  Cd  and  cd,  but  cd  and  dE  are  usually 
made  continuous  and  should  therefore  be  the  some  size. 
2Ls  2y2"X2/'X1/4"  will  answer  for  these,  the  net  area  being 
2X1.07— 2X1/4X(%+1/8)=1.76  sq.  in.  For  light  trusses  a& 
and  be  are  also  usually  made  continuous.  The  sizes  of  the  other 
tension  members  are  easily  determined,  as  shown  in  the  table 
above. 


88  THE  DESIGN  OF  A  EOOF.  Art.  40. 

We  will  try  to  make  each  of  the  compression  members  of  two 
angles.  These  will  be  back  to  back,  and  will  be  far  enough 
apart  to  admit  the  connection  or  gusset  plates  between  them  at 
the  joints.  We  will  try  to  make  all  gusset  plates  %  in.  thick.  The 
radius  of  gyration  for  the  various  sizes  of  angles  may  be  taken 
from  Cambria,  pages  189  to  193.  The  least  width  of  compression 
member  allowed  is  -^  of  the  length  (Spec.  Art.  59),  therefore 
2"X2"Ls  cannot  be  used  in  compression  members  whose  length 
is  greater  than  100  in.=8.3  ft.  For  Bb  and  Dd  we  will  try 
2Ls2"X2"X1/4".  The  least  radius  of  gyration  is  0.61.  The 

f\  f\ 

maximum  allowed  units  tress  is  12500— 500-  —=7900  Ibs.  per 

0.61 

7000 
sq.  in.     The  required  area  will  be  =0.89  sq.  in.,  while  the 

7900 

actual  area  is  1.88  sq.  in.,  and  therefore  Bb  -and  Dd  may  be 
made  of  2Ls  2"X2"X1/i". 

For    Cc   the    least    allowable   width  -of   member   will   be 

11  3X12 

—  =2.71  in.     The  least  angles  that  can  be  used  will  be 
60 

2Ls  3"X2%"X*4"  unless  "special"  angles  are  used,  which  us- 
ually take  longer  for  delivery  from  the  mills  and  might  thus 
delay  the  work.  The  table  of  column  unit  stresses  on  page  15 
of  the  specifications  may  be  used  instead  of  applying  the  column 
formula  each  time.  Trying  2Ls  3"X2%"X%"  for  Cc,  the  least 

radius  of  gyration=0.95   and  —  = — —=11.9.     Allowed  unit 

T        0.95 

stress  from  table=6,550  Ibs.  per  sq.  in.     The  required  area= 

i^-°  =  2.14  sq.  in.  The  actual  area==2X  1.32=2.64  sq.  in., 
6550 

which  is  sufficient. 

The  rafter  should  be  made  continuous  from  eave  to  ridge, 
if  this  length  is  not  too  great,  say  over  60  ft.  It  must  be  pro- 
portioned for  direct  compression  and  bending,1  The  maximum 
compression  occurs  in  aB,  and  the  bending  in  this  case  is  also 
a  maximum  in  this  panel,  or  nearly  so.  aB  is  loaded  trans- 
versely by  the  purlins,  as  shown  in  Fig.  34.  Considering  the 


Tor  a  complete  discussion  of  this  subject  see  Heller's  "Stresses 
in  'Structures,"  Art.  111. 


Art.  40. 


THE  DESIGN  OF  A  ROOF. 


89 


member  as  a  simple  beam  supported  at  a  and  B,  the  maximum 
moment  will  be  2509X3.55=8907  ft.  Ibs. 

The  rafter  is  not  really  in  the  condition  of  a  beam  simply 
supported  at  the  ends,  nor  are  the  ends  fixed,  because  the  con- 
nections are  elastic.  The 
actual  moment  lies  some- 
where between  that  for 
the  two  conditions  of  free 
and  fixed  ends,  (Spec.  Art. 
16)  and  may  safely  be 
taken  -as  %  of  the  moment 
for  a  simple  beam.  We 
have  then  Jf=%X8907= 
Fig.  34.  5567  ft.  lbs.=66800  in.  Ibs. 

This  is  the  positive  moment  under  the  load  nearest  the  middle. 
There  is  also  a  negative  moment  at  each  support  which  may  be 
assumed  to  be  equal  to  the  same  'amount,  consequently  in  apply- 
ing the  formula  of  Art.  16  of  the  Spec.,  the  factor  n  must  be 
taken  as  the  greatest  distance  from  the  neutral  axis  to  the 
extreme  fiber. 


I        A 
=33.18.       n=S. 


A=2X4.5=9.0.      «= 


1=2X16.59 


66800X3.92    ,    61100 


33.18  9.0 

=7891+6789=14680  Ibs.  per  sq.  in.  The  allowed  fiber  stress 
is  15000  Ibs.  per  sq.  in.,  therefore  these  angles  are  large  enough. 
If  the  next  size  smaller  angle  be  tried  it  will  bo  found  too  small. 
The  laterial  struts  do  not  carry  much  stress,  and  their  size 
is  determined  by  Art.  59  of  the  specifications,  which  requires 
that  their  least  width  be  not  less  than  ^  of  their  length.  This 
requires  the  use  of  members  not  less  than  4.8  in.  wide.  The 
most  economical  section  will  be  2Lc  5"X3"X  A",  the  longer  legs 
being  back  to  back.  The  ridge  strut  is  usually  made  the  same 
for  all  bays.  The  bottom  chord  ties  take  no  definite  stress,  but 
should  not  be  less  than  one  angle  3%"X3"X&"  with  the  3^ 
inch  leg  vertical.  All  the  laterals  may  be  %  in.  round  rods. 
The  vertical  member  of  the  truss  at  the  middle  takes  no  stress, 
but  keeps  the  lower  chord  from  sagging. 


Fig.  35. 


Sheet  No.  _/_ 
Estimate  for. 


THE  OHIO   STATE   BRIDGE  COMPANY 

Made  by. G.  7L&  .  .  Date  .  _  £_r<^ 


5pan  Extreme ££-/_.. 

Roadway 

Sidewalk 

Capacity  Trusses 

Capacity  Floor 

Specifications 


Span  C.  to  C._ 

//  Panels  at 

Depth  C. 

Length  <*£&&.  22L- 


Sec. 


Estimated  |    (Steel 

DL  per  ft. }    |  Floor  &  Track -, 


Total 

Panel  Load  per  Truss  Dl 

LL_. 


Total  Steel 
Steel  per  ft. 
Total  Lumber 


/Qc 


X 


y< 


40  /S.3  455 


72. 


204.-S 


30.0 


&-J3a 


32 


2.06.6  0.83 


2oA\/.o 


Dr? 


U&L 


70 


-Ko 


/.*5"  36.Q 


173 


far. 


40 


#0 


02  THE  DETAIL  DRAWINGS.  Art,  41. 

Having  completed  the  designing  of  the  members,  what  is 
known  as  the  stress  sheet  (21)  is  usually  next  made.  This  is 
ordinarily  a  line  diagram  «as  shown  in  Fig.  35,  on  which  are 
written  the  stresses  and  sizes  for  all  the  members,  as  well  as  the 
general  dimensions. 

The  estimate  of  weight  miay  now  be  made,  so  that  the  cost 
estimate  may  be  made  up  preparatory  to  letting  the  contract. 

41.  The  Detail  Drawings.  (27)  The  detail  shop  drawings 
are  made  by  the  contractor  and  should  be  submitted  to  the  pur- 
chaser's  engineer  for  approval. 

To  avoid  eccentric  stresses  the  center  of  gravity  lines  of  all 
members  coming  together  at  a  joint  should  intersect  in  one 
point.  This  is  not  practical  in  roof  trusses  because  the  drawings 
and  templet  work  would  be  too  complicated.  Instead  of  using 
the  gravity  lines  as  center  lines,  the  rivet  gage  lines  'are  used. 
For  members  composed  of  2Ls  2"X2"X:/4"  the  gravity  line  is 
0.59  in.  from  the  backs  of  the  angles,  while  the  rivet  line  is 
1%  in.  out.  This  makes  the  eccentricity  of  the  connection  0.535 
in.  For  a  member  composed  of  two  angles  31/2/rX31/2//XiV/ 
the  eccentricity  is  2.00—0.99=1.01  in.  For  an  angle  having 
two  gage  lines,  the  center  should  of  course  be  taken  on  that  rivet 
line  which  is  nearest  the  gravity  line.  For  a  member  composed 
of  2Ls  6"X3y2"X%"  the  center  of  gravity  is  2.08  in.  from  the 
back  of  the  shorter  leg.  The  rivet  lines  in  a  6  inch  leg  may  be 
spaced  2  in.  and  4%  in.  fom  the  back  of  the  angle,  and  of  course 
the  inside  gage  line  should  'be  used  as  the  center  line. 

In  a  roof  truss  it  is  the  common  practice  to  have  the  center 
lines  of  the  members  intersect  in  a  single  point  iat  each  joint 
except  the  shoe  joint  a,  Fig.  36. 

In  order  to  take  the  reaction,  the  truss  must  have  an  appre- 
ciable depth  at  the  end.  This  result  is  usually  accomplished  by 
making  the  intersection  of  the  center  lines  of  the  rafter  and 
.bottom  chord  come  at  some  little  distance  beyond  the  center  of 


Art.  41. 


THE  DETAIL  DRAWINGS. 


93 


the  bearing  plate,  as  shown  in  Fig.  36.  To  facilitate  the  driving 
of  the  rivets  in  the  shoe  plate  <and  in  the  purlin  connection  the 
depth  >at  the  end  should  be  about  6  inches.  The  distance  from 
the  center  of  the  bearing  to  the  intersection  is  usually  made  such 
an  amount  as  will  avoid  odd  fractions  of  an  inch  in  the  center 
lengths. 


Fig.  36a. 


This  method  of  detailing  the  joint  at  the  shoe,  while  the  most 
common  is  not  the  best,  las  it  introduces  eccentric  stresses  into 
the  members,  causing  bending  in  them  and  twisting  on  the 
rivets  of  the  joint. 

A  better  but  slightly  more  expensive  detail,  is  shown  in 
Fig.  36a,  in  which  the  center  lines  of  the  stresses  at  this  joint 
intersect  in  <a  single  point. 

Having  determined  this  point  by  scale,  the  slope  of  the 
center  line  of  the  rafter  is  made  exactly  6  in.  vertical  to  12  in, 
horizontal,  for  a  %  pitch  roof. 

The  usual  standard  size  of  shop  drawings  is  24"X36".  The 
border  line  should  be  a  single  heavy  line  placed  14  inch  from 
the  line  on  which  the  tracing  is  trimmed.  (Or  see  Fig.  25.) 


94  THE  DETAIL  DRAWINGS.  Art.  41. 

The  truss  outline  and  the  details  are  not  drawn  to  the  same 
scale.  This  amounts  to  drawing  the  detail  of  each  joint  separ- 
ately and  then  assembling  the  joints  into  the  form  of  a  truss. 
It  is  not  necessary  to  show  the  members  broken  between  joints, 
although  the  distances  are  not  to  scale.  Any  rivet  spacing 
between  panel  points  cannot  be  drawn  to  scale,  but  it  is  not 
necessary  to  show  all  the  rivets  if  the  figures  locating  them  are 
properly  given.  The  scale  for  details  is  usually  1  in.  or  iy2  in. 
per  ft.,  depending  upon  the  -available  room.  The  larger  scale 
is  easier  to  work  with,  especially  for  the  beginner.  The  scale 
for  the  center  lines  should  be  so  selected  that  there  will  be 
sufficient  room  for  the  elevation  of  half  the  truss,  the  dimension 
lines,  the  top  view  of  the  rafter  and  the  sectional  view  of  the 
bottom  chord,  with  all  connections  for  purlins,  laterals,  etc.  The 
scale  for  the  details  must  be  decided  upon  first.  A  sample 
drawing  should  be  consulted  and  studied,  'and  if  necessary  pre- 
liminary sketches  made  of  the  lateral  connections.  Compact- 
ness is  desirable,  but  crowding,  especially  of  dimension  lines, 
should  be  avoided.  Usually  the  scale  for  the  outline  should  not 
be  less  than  one  half  that  of  the  details. 

Usually  on  the  same  sheet  with  the  truss  there  is  put  a  dia- 
gram of  the  roof  showing  the  location  of  trusses,  bracing,  etc., 
similar  to  Fig.  35.  This  is  called  an  erection  diagram.  In  a 
building  with  steel  columns  and  other  steel  work,  the  erection 
diagram  usually  occupies  a  sheet  by  itself.  Sometimes  there  is 
also  sufficient  room  on  the  sheet  with  the  truss  drawing  for 
drawings  of  struts,  purlins,  etc. 

After  the  scales  have  been  determined,  one  half  the  dis- 
tance between  the  interactions  of  the  center  lines  of  the  rafters 
and  bottom  chord  (40' — 101/2"  in  our  case)  is  laid  off  horizon- 
tally to  the  smaller  scale  chosen  for  the  outline,  and  one  half 
of  this  distance,  if  the  roof  has  %  pitch,  (20'— 5%")  is  laid 
off  vertically  -at  the  right  end,  this  being  the  rise  of  the  center 
line  of  the  rafter  above  the  bottom  chord.  Now  the  hypotenuse 
of  the  right  triangle  is  drawn,  which  is  the  center  line  of  the 
rafter.  This  center  line  is  then  divided  into  four  equal  spaces, 
and  the  center  lines  of  the  members  Bb,  Cc  and  Dd  are  drawn 
perpendicular  to  it.  The  intersections  of  Bb  and  Cc  with  the 
bottom  chord  determine  points  ~b  and  c,  and  of  Dd  with  cE,  point 


Art.  41.  THE  DETAIL  DRAWINGS.  95 

d.  The  length  of  Cc  is  twice  that  of  Bb  and  Dd,  and  equals  &B. 
The  lengths  of  ab,  be,  bC,  Cd,  cd  and  dE  are  equal.  Thus  it  is 
seen  that  the  center  lengths  are  very  easily  determined,  as  given 
in  Fig.  36,  from  right  triangles. 

Joint  a.  Fig.  36  is  a  shop  drawing  of  the  truss.  The  forces 
acting  at  joint  a  are  the  rafter  stress,  the  bottom  chord  stress, 
the  purlin  load  and  the  reaction.  There  must  be  enough  rivets 
in  the  joint  to  safely  transmit  these  forces.  To  avoid  changing 
punches,  (6)  the  rivets  will  be  made  %  in.  throughout.  (Maxi- 
mum size  for  a  2  in.  leg.)  Joint  a  has  larger  stresses  than  any 
other,  and  if  %  in.  connection  plates  were  used  throughout  it 
would  result  in  a  large  gusset  here,  consequently,  (5)  we  will 
use  a  y2  in.  gusset  plate  at  a  and  make  all  the  others  %  in. 

The  rafter  stress  is  61,100  Ibs.  The  value  of  -a  %  in.  rivet 
in  double  shear  is  6136  Ibs.  (This  value  is  less  than  the  bearing 
value  on  a  %  in.  plate).  The  number  of  rivets  required  in  the 

rafter  connection=-  -  =10  rivets.      We  will  have  to  add  an 
6136 

extra  rivet  to  transfer  the  purlin  load,  this  makes  11  rivets.  The 
rivets  immediately  over  the  bearing  plate  in  the  bottom  chord 
must  transfer  the  vertical  component  of  the  rafter  stress  and 
the  purlin  load  to  the  bottom  chord  angles  which  rest  on  the 
bearing  plate. 

The  amount  of  this  reaction  will  be  4X7800=31200  Ibs., 

and  the  number  of  rivets  required  =  -  =  5.    In  addition  to 

6138 

these  we  must  have  in  the  bottom  chord  sufficient  rivets  to  trans- 

fvlfiOO 

fer  the  bottom  chord  stress,  54600  Ibs.    This  requires^         ^~9 

6136 

rivets,  making  a  total  of  14  rivets  in  the  bottom  chord  connec- 
tion. If  the  reaction  acted  equally  on  all  the  bottom  chord 
connection  rivets  at  this  point,  the  connection  would  only  have 
to  be  proportioned  for  the  resultant  of  the  two  stresses 


V546002  +  312002=62900  Ibs.,   and  the  rivets  required  would 
only  be  =^  =  11  rivets. 


It  is  not  good  practice  to  put  the  rivets  closer  together  than 
2%  in.,  and  they  must  not  come  nearer  the  edge  of  any  piece 
than  1*4  in.  (7).  Care  must  be  exercised  to  see  that  the  rivets 


96  THE  DETAIL  DRAWINGS.  Art.  41. 

in  opposite  legs  of  angles  stagger  so  that  one  rivet  head  does  not 
'interfere  with  the  driving  of  the  other  rivet. 

Joint  C.  At  this  point  the  components  of  the  stresses  in 
bC  'and  Cd,  parallel  to  the  rafter,  balance  each  other  in  the  plate 
and  require  no  rivets  in  the  rafter.  The  components  perpendi- 
cular to  the  rafter  must  be  transmitted  to  Cc.  Their  sum  is 
7000  Ibs.,  which  may  be  gotten  by  laying  off  the  stresses  and 
scaling  the  components  parallel  to  Cc.  The  balance  of  the  stress 
in  Cc  (=7000  Ibs.)  comes  directly  from  the  rafter.  These  to- 
gether require =3  rivets  in  bearing  on  the  %  in.  gusset 

4690 

plate.  There  must  be  -a  sufficient  number  of  rivets  through  the 
rafter  angles  to  transmit  the  7000  Ibs.  More  are  put  in  here 
so  as  not  to  exceed  the  maximum  allowed  pitch. 

It  will  be  noted  that  the  rivet  spacing  dimension  line  for 
each  member  starts  at  the  center.  A  connection  by  a  single  rivet 
should  never  be  used,  and  preferably  at  least  three  rivets  should 
be  used  in  any  connection. 

Joint  c.  A  -splice  is  made  here  in  the  bottom  chord  because 
it  changes  section,  and  it  is  made  a  field  splice  because  the  truss 
is  too  large  to  ship  in  one  piece.  Each  truss  is  shipped  in  four 
pieces.  The  middle  section  of  bottom  chord  and  the  vertical 
member  Ee  are  two  of  these.  The  greatest  depth  of  any  piece 
will  then  be  over  12  ft.  at  Cc,  and  this  can  not  be  handled  by 
all  railroads.  (31) 

The  horizontal  components  of  Cc  and  cd  act  toward  the 
right  and  their  sum,  equal  to  15600  Ibs.,  must  be  transmitted  to 
be.  (15600  Ibs.  is  the  difference  in  the  stresses  in  be  and  ce.) 

15600 
This  requires   •  =  4  rivets  in  bearing  on  the  %  in.  gusset 

31200 
plate.      The  bottom  chord  splice  will  require  =  11  rivets 


in  single  shear.  We  must  have  11  rivets  on  each  side  of  the 
splice,  in  the  splice  plate,  which  also  acts  as  a  connection  for  the 
bottom  chord  rods,  strut  and  tie.  The  three  rivets  through  ce 
and  the  gusset  plate  are  not  counted  as  a  part  of  the  splice 
(Spec.  Art.  38)  but  are  put  in  because  there  should  be  a  connec- 
tion between  the  vertical  as  well  as  the  horizontal  legs  of  the 
angles.  The  splice  plate  should  have  'as  much  net  section  as  the 


6 

CK 

X 

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Fig. 


Art.  41.  THE  DETAIL  DRAWINGS.  97 

angles  of  ce.  Even  with  the  minimum  thickness  of  plate  allowed 
there  is  a  large  excess  in  this  case. 

Lateral  Connections.  The  lateral  connections  should  be 
sufficient  to  take  the  full  value  of  the  area  of  a  %  in.  rod  at 
18000  Ibs.  per  sq.  in.  (Spec.  Art.  13).  We  have  then  0.44X18000 
=7900  Ibs.  If  we  use  a  1%  in.  pin  for  the  lateral  rods  which 
have  forked  loops,  the  allowed  bearing  pressure  of  the  pin  on 
the  %  in.  plate  will  be  *4X13/4X 25000=10900  Ibs. 

It  is  very  essential  that  clearance  be  provided  where  two 
members  come  together,  except  where  tight  joints  are  required, 
as  in  the  bottom  chord  splice  and  at  the  ridge.  The  usual  mini- 
mum clearance  of  members  is  %  in. 

Rivet  holes  are  made  ^  in.  larger  in  diameter  than  the  size 
of  the  rivet  to  be  used.  In  roof  work  for  lateral  connections, 
pin  holes  are  usually  punched,  and  are  made  fs  in.  larger  than 
the  pin.  Sizes  of  all  rivets  and  holes  must  be  plainly  marked 
on  the  drawings. 

The  exact  length  of  each  piece  must  be  given  with  its  other 
dimensions.  The  length  should  invariably  be  given  last.  The 
width  of  a  plate  should  be  given  first  and  the  longer  leg  of  an 
angle  should  be  given  first,  thus,  1_15"X%"X1'— 7%", 
2Ls4"X3//XTV'X21/-7i/4".  The  width  of  a  plate  should  al- 
ways be  given  in  inches,  and  should  not  contain  a  fraction  lass 
than  !/4  in. 

For  the  use  of  the  templet  maker,  the  bevel  of  each  in- 
clined line  of  rivet  holes  should  be  given.  The  longer  dimension 
of  the  bevel  is  usually  made  V— 0".  All  dimensions,  other  than 
the  widths  of  plates,  of  one  foot  or  more  should  be  given  in  feet 
and  inches,  and  not  in  inches  alone,  thus  V— 1-^V'  and  not 

ISA". 

While  no  dimension  is  ever  to  be  taken  by  scale,  off  a  shop 
drawing,  it  is  nevertheless  essential  to  draw  by  scale.  This  can 
not  be  done  unless  the  drawing  is  worked  up  in  a  logical  man- 
ner. A  draftsman  who  makes  many  erasures  will  seldom  be- 
come interested  enough  in  his  work  to  be  a  success.  Rivet  heads 
and  rivet  holes  should  be  drawn  to  scale. 

Accuracy  is  essential,  but  no  smaller  fraction  than  ^  of  an 
inch  is  ever  used  in  structural  work.  If  a  line  of  spacing  should 
add  up  10'— 64|",  10'— 6y2"  will  not  answer. 


98  THE  DETAIL  DRAWINGS.  Art.  41 

All  spacing  must  be  continuous  from  center  to  center,  and 
the  different  sets  of  spacing  should  be  kept  separate  and  in 
straight  lines,  if  possible,  not  offset  lines.  First  we  have  the 
general  dimensions  such  as  span  and  length  of  rafter,  center  to 
center;  second,  we  have  the  distance  center  to  center  for  each 
member;  third,  we  have  the  rivet  spacing  which  must  be  con- 
nected with  the  centers;  and  fourth,  we  have  the  open  holes, 
which  should  be  connected  up  for  the  benefit  of  the  inspector. 
If  there  are  holes  in  both  legs  of  an  angle,  there  must  be  two 
lines  of  spacing. 

Each  rivet  hole  must  be  located  definitely,  cuts  on  plates 
shown,  and  bevels  of  center  lines  given.  The  gages  of  all  rivet 
lines  must  be  given. 

The  good  appearance  of  a  drawing  goes  far  to  inspire  con- 
fidence in  its  accuracy.  It  should  be  workmanlike.  The  ap- 
pearance of  a  drawing  depends  largely  upon  the  lettering  and 
general  arrangement.  Except  in  the  title,  the  letters  should  all 
be  free  hand  and  of  a  plain  style.  The  figures  should  be  par- 
ticularly clear.  Figures  and  letters  should  not  all  be  the  same 
size.  The  dimensions  of  a  main  member  should  be  in  larger 
figures  than  those  for  a  detail,  and  center  distances  larger  than 
rivet  spacing.  It  is  essential  that  the  sizes  of  plates,  angles,  etc., 
be  in  the  best  possible  place  for  them.  Shop  men  are  not  sup- 
posed to  be  able  to  read  a  drawing  as  readily  as  a  draftsman 
or  templet  maker.  To  become  a  proficient  letterer,  persistent 
practice  is  necessary,  and  will  work  a  wonderful  improvement 
in  any  man's  work.  (27) 

The  title  and  sheet  number  should  be  in  the  lower  right 
hand  corner,  if  possible.  The  name  of  the  draftsman  and  the 
date  when  the  drawing  was  finished,  should  appear  in  the  title, 
«us  well  as  a  statement  of  what  is  shown  on  the  drawing.  (See 
Fig.  24.) 


CHAPTER  V. 
PLATE  GIRDER  BRIDGES. 

42.  Construction  and  Uses.  A  plate  girder  is  a  built  up 
I-beam.  It  consists  of  a  single  web  plate1  and  two  flanges  (top 
and  bottom)  riveted  together.  Each  flange  may  be  'composed 
of  two  angles,  two  angles  and  one  or  more  cover  plates,  two 
angles  with  side  and  cover  plates  or,  in  very  heavy  girders,  four 
angles  with  side  and  cover  plates  in  various  combinations.  Fig. 
37  shows  some  common  flange  sections.  Types  (e)  and  (f)  are 
frequently  used  for  crane  girders  where  a  load  is  applied  along 
the  edges  of  the  flange. 


Fig.  37. 


(f) 


Plate  girders  are  used  in  buildings  and  bridges  where  some- 
thing larger  than  a  rolled  I-beam  or  I-beam  girder  is  required. 
In  buildings  they  are  used  for  floor  and  crane  girders  and  in 
bridges,  for  stringers  and  floor  beams,  and  for  the  girders  of 
plate  girder  bridges. 

Plate  girder  bridges  are  seldom  built  for  spans  of  more  than 
100  ft.,  though  some  have  been  built  over  130  feet  long.  The 
railways  use  them  almost  exclusively  for  spans  from  30  ft.  to 
100  ft.,  when  steel  bridges  are  used,  and  many  of  the  better  class 
of  highway  bridges  of  these  lengths  are  plate  girders. 

A  plate  girder  bridge  is  usually  considered  to  be  the  most 
durable  kind  of  metal  bridge. 

43.  Stresses  in  Girders.2  A  plate  girder  is  treated  as  a 
solid  beam  and  the  stresses  are  investigated  by  the  method  of 


1W!hen  two  web  plates  are  used  a  few  inches  apart,  it  is  called 
a  box  girder." 

2  See  Heller's  Stresses  in  Structures,"  Art.  75,  page  111. 


100  STRESSES  IN  GIRDERS.  Art.  43. 

sections,1  the  stresses  acting  upon  a  cross  section  being  the  ones 
usually  found. 

The  loads,  including  the  weight  of  the  girder  itself,  which  a 
girder  carries,  together  with  the  reactions  produced  by  them,  are 
usually  a  series  of  forces  parallel  to  the  cross  section  of  the 
girder,  and  are  equivalent  to  a  resultant  shear  at  the  section  and 
a  couple ;  these  are  held  in  equilibrium  by  a  shearing  stress  and 

a  couple  acting  in 
opposite  directions 
.  at  the  section.  This 
is  illustrated  in  Fig. 
38,  in  which  R  at  c 
is  the  resultant  of  all 
r,  forces  to  the  left  of 
the  section  mn  and  is 
equivalent  to  the 
shear  R  at  the  sec- 


L±J 


Fig.  3&2  tion  an(j  faQ   COUpie 

whose  moment  is  Ra  and  is  called  the  bending  moment.  These 
are  resisted  by  a  shearing  stress  S,  equal  to  R  and  a  moment  of  a 
couple  Fd=Ra.  Since  the  bending  moment  is  the  moment  of  a 
couple,  the  moment  of  the  bending  stresses  must  also  be  that 
of  a  couple.  The  forces  F  are  the  resultants  of  the  tensile  and 
compressive  forces  acting  on  the  section,  whose  intensities  vary 
uniformly  from  zero  at  the  neutral  axis  to  a  maximum  intensity 
at  the  top  and  bottom.  Since  the  greater  part  of  the  area  of  the 
cross  section  is  in  the  flanges  and  the  intensities  are  greatest  at 
the  top  and  bottom,  the  resultants,  F,  come  near  the  top  and  bot- 
tom of  the  girder,  making  d  large.  Fd  is  the  moment  of  resist- 
ance, and  it  is  well  to  remember  that  it  is  equivalent  to  the 
moment  of  a  couple,  and  that  both  the  web  and  flanges  resist 
bending. 

44.  The  Web.  It  is  not  known  just  how  the  shearing 
stresses  are  distributed  over  an  I  cross  section.  We  know  that 
their  intensities  must  be  zero  at  the  upper  and  lower  edges  of 


Heller's  "Stresses  in  Structures,"  Art.  64,  page  85. 
8  See  Heller's  "Stresses  in  Structures,"  Fig.  65,  page  86. 


Art.  44.  THE  WEB.  101 

the  girder,  and  are  a  maximum  at  the  neutral  axis.1  The  law 
of  variation  between  these  extremes  depends  upon  the  cross 
section.  For  an  I  cross  section,  the  usual  assumption  that  the 
shearing  stress  is  uniformly  distributed  over  the  area  of  the  web 
only,  will  give  an  intensity  of  shearing  stress  which  will  usually 
be  greater  than  the  actual  maximum.2  The  flanges  form  a  large 
part  of  the  cross  section  and  must  carry  considerable  shear. 

It  is  therefore  always  assumed  that  the  web  carries  all  of 
the  shear3  and  that  its  intensity  is  uniform. 

Aw       flt=      ^—  r.-.  .  .,-.—«   [•:•'•  ••••  •  (1) 

Equation  (1)  will  determine  the  minimum  area  of  web  per- 
missable.  Its  thickness  is  never  made  less  than  *4  inch  and 
seldom  less  than  %  inch.  It  must  be  made  thick  enough  to  give 
sufficient  bearing  for  the  rivets  which  connect  the  flanges  to  it, 
and  this  consideration  frequently  determines  its  thickness.5 

The  depth,  h,  is  determined  by  considerations  of  economy  as 
explained  in  Art.  46,  or  by  local  conditions. 

When  there  are  splices  in  the  web,  it  is  not  strictly  correct 
to  take  the  gross  area  as  effective  in  resisting  shear.  It  may  be 
assumed  that  the  rivets  of  the  first  row  in  the  splice  take  up 
one  half  of  their  proportion  of  the  shear  on  one  side  of  the  plane 
through  the  center  of  the  row.  (4)  Then  the  net  section  of  the 
web  through  this  row  should  be  sufficient  to  take  the  balance  of 
the  shear.  This  would  make  equation  (1)  read  as  follows: 
Smax— y2  Value  of  Rivets  in  Row 

SB 

Formula  (2)  is  not  used  in  practice,  and  the  difference  in 
the  result  by  the  two  is  usually  negligible. 


JFor  a  discussion  of  this  subject  on  the  assumption  that  a  sudden 
change  in  width  of  the  cross  section  has  no  effect  upon  the  distribu- 
tion of  the  shearing  stress,  see  Johnson's  "Modern  Framed  Struc- 
tures," Chapter  VIII,  Art.  130,  page  145. 

,See  also  Rankine's  "Applied  Mechanics,"  Art.  309,  page  338. 

2  See  Heller's  "(Stresses  in  Structures,"  Art.  71,  page  105. 

3  When  the  flanges  are  inclined,  they  carry  a  part  of  the  shear. 

4  See  Heller's  "Stresses  in  Structures,"  Bq.  33,  page  111. 

6  See  an  article  by  C.  H.  Wood  in  Eng.  News,  Aug.  6,  1908. 


102  THE  FLANGES.  Art.  45 

The  web  resists  considerable  bending  moment,  as  will  be 

seen  if  the  formula  M==  — w)1 

is  considered.  If,  for  example,  the  moment  of  resistance  of  the 
web  is  |  of  the  total  moment  of  resistance  of  the  cross  section, 
the  web  will  resist  |  of  the  total  bending  moment  and  the  flanges 
will  resist  f  of  it.  The  resultant  of  the  two  kinds  of  stresses 
in  the  web  is  never  calculated,  but  to  compensate  for  this,  it  is 
often  assumed  that  the  flanges  take  all  the  bending  stresses, 
which,  of  course,  has  the  effect  of  making  them  larger  and  thus 
reducing  the  stress  in  the  web.  But  if  it  be  remembered  that 
the  shear  is  not  a  maximum  where  the  bending  is,  it  will  be  seen 
that,  theoretictally,  this  increase  of  flange  section  is  not  neces- 
sary. 

45.  The  Flanges.  The  bending  stresses  in  a  girder  may 
be  provided  for  by  making  the  cross  section  such  that  the  ex- 
treme fiber  stress,  given  by  equation  (3)  will  not  exceed  the 
maximum  allowed  unit.  This,  however,  involves  much  labor, 
as  there  are  no  complete  tables  of  section  moduli  of  plate  girders 
as  there  are  of  I-beams,  and  the  solution,  involving  the  two  un- 
known quantities  I  and  v,  must  be  by  trial. 

When  the  flanges  are  alike,  as  they  usually  are,  the  solution 
is  very  much  simplified  by  making  two  assumptions:2 

"1.  The  stresses  in  the  flanges  (tension  and  compression) 
are  uniformly  distributed  over  their  areas  and  their  resultants, 
(F,  Fig.  38)  therefore,  act  at  the  center  of  gravity  of  these  areas. 

"2.  That  the  depth  of  the  web  h,  may  be  set  equal  to  d, 
the  distance  between  the  centers  of  gravity  of  the  flanges." 

Granting  these,  it  is  easily  shown  that  the  moment  of  re- 
sistance of  the  web  is  equal  to  the  moment  of  resistance  of  % 
of  the  web  area,  concentrated  at  the  center  of  gravity  of  each 
of  the  flanges. 


'For  derivation  see  Heiller's  "Stresses  in  Structures,"  Art.  66, 
page  89. 

'See  Heller's  "Stresses  in  Structures,"  Art.  75,  page  111,  for  a 
complete  discussion. 


Art.  45.  THE  FLANGES.  103 

Then  we  have 

M 

Equivalent  Flange  Stress=  •JJT  ......................  (4) 

Equiv.  Fig.  Stress  f 

Equivalent  Flange  Area=  —       ~  ~  .........  (&) 


Beqd.  Flange  Area  proper  (Net  Area  one  Flange) 

=Equiv.  Fig.  Area—yQAw  .....  .............  r.,(6) 

If,  for  any  reason,  there  are  vertical  lines  of  rivet  holes  in 
the  web,  its  moment  of  resistance  is  decreased,  and  this  is  some- 
times taken  into  account  by  modifying  Eq.  (6)  as  given  in  equa- 
tion (7)  below,1 

Reqd.  Flange  Area  proper  (Net  Area  one  Flange) 

=Equiv.  Fig.  Area—y8Aw  .....  .  .  .  ...........  (7) 

The  effect  of  the  rivet  holes  on  the  moment  of  resistance  of 
the  web  may  be  easily  calculated. 

Some  specifications  require  that  all  of  the  bending  stresses 
shall  be  considered  as  being  resisted  by  the  flanges,  in  which  case 
the  equivalent  flange  area  as  given  by  equation  (5)  becomes  the 
required  net  flange  area  proper. 

Since  d,  the  effective  depth,  cannot  be  calculated  until  the 
flanges  are  known,  an  approximate  value  must  be  used  on  the 
first  trial.  Two  or  three  trials  will  usually  give  a  flange  which 
is  practically  exact. 

In  equation  (5)  the  working  stress  for  the  tension  flange  is 
used,  thus  giving  the  required  net  area  of  that  flange.  (See 
Art.  11  for  allowance  to  be  made  for  rivet  holes.)  The  top 
flange  is  usually  made  the  same  as  the  bottom  flange  (gross  areas 
alike)  but  it  must  be  held  so  that  it  will  not  buckle  sidewise.2 
(See  Art.  51  and  52.) 

46.  Economic  Depth.3  The  most  economical  depth  of  a 
plate  girder  is  usually  the  least  weight  depth.  It  depends  upon 
a  number  of  conditions  and  may  be  easily  calculated,  theoreti- 
cally, when  these  conditions  are  known.  The  calculated,  economic 


'See  Specifications  of  the  "American  Railway  Engineering  and 
Maintenance  of  Way  Association."  for  Steel  Railroad  Bridges,  1906, 
Art  27. 

'See  Spec,  of  the  Am.  Ry.  Eng.  and  M.  of  W.  Assoc.,  Arts.  28 
and  78.  Also  Cooper's  Spec,  for  Steel  Railway  Bridges,  1906,  Art.  79. 

•See  Johnson's  "Modern  Framed  Structures,"  Art.  285,  page  332. 


104  ECONOMIC  DEPTH.  Art.  46. 

depth  is  seldom  used  exactly,  on  account  of  local  conditions  and 
practical  limitations,  and  is  to  be  regarded  merely  as  a  general 
guide.  A  variation  in  depth  of  as  much  as  10%  or  15%  will 
usually  not  change  the  total  weight  of  the  girder  appreciably. 

Formulas  will  now  be  deduced  for  the  economic  depth  for 
the  following  three  conditions  as  to  flange  section  : 

(a)  When  %  of  the  web  area  is  .considered  in  each  flange. 

(b)  When  %  of  the  web  area  is  considered  in  each  flange. 

(c)  When  none  of  the  web  area  is  regarded  as  flange  area. 
The  girder  will  be  -assumed  of  constant  cross  section  from 

end  to  end. 

(a)     When  %  of  the  web  area  is  regarded  as  flange  area. 
The  gross   area  of  the   cross  section  of  the   gird 

%Af  -\-rivet  holes.   From  equations  (4)  and  (6),  AF  ~7/~ 
and  then  we  have,  setting  h=d, 


A=dt+  -'-  --  i/3dt-}-rivet  holes. 
dst 

The  gross  area  of  the  flanges  may  be  taken  as  15%  greater 
than  the  net  area,  which  gives  : 


As  the  weight  varies  directly  with  the  cross  section,  for  a 
least  weight  depth  we  may  differentiate  this  expression  with 
respect  to  d  and  set  the  first  derivative  equal  to  zero. 


dd  sf  d2 

.  ,  .  ,  . 

from  which  d2=—        —  and 

0.617*  t 


(&)     When  %  the  web  is  taken  as  flange  area,  equation  (8) 
becomes 


dE=1.80    .    _ 


(c)     When  no  web  is  considered  as  flange  area,  equation 
(8)  becomes 


Art.  47.  STIFFENEBS  106 

When  the  flange  section  is  not  constant  for  the  entire  length 
of  the  girder,  the  economic  depth  will  be  somewhat  less  than 
that  given  by  the  above  formulas,  and  will  vary  with  the  propor- 
tion of  cover  plates,  stiffeners,  and  web  splices.  The  following 
equation  will  give  the  least  weight  depth  as  close  as  a  general 
formula  can  give  it. 


47.  Stiffeners.  The  lines  of  maximum  compression  in  a 
plate  girder  web,  cross  the  neutral  axis  at  an  angle  of  45°  and 
extend  downward  toward  the  supports  from  the  middle.1  The 
tendency  of  the  web  plate  to  buckle  under  these  compressive 
stresses  is,  in  part,  resisted  by  the  equal  tensile  stresses  at  right 
angles  to  them.  Just  what  the  resulting  effect  on  the  web  is,  is 
not  well  understood,  but  when  the  ratio  of  the  depth  of  the  web 
to  its  thickness  is  great  (exceeds  about  50  or  60)  it  must  be 
stiffened.  Of  course  the  requirement  of  stiffeners  depends  upon 
the  amount  of  shear  at  the  point.2 

Stiffeners  are  placed  vertically  on  account  of  ease  of  manu- 
facture. They  would,  perhaps,  serve  their  purpose  better  if 
placed  parallel  to  the  line  of  the  compressive  stresses,  but  if 
placed  vertically  and  not  more  than  the  depth  of  the  girder 
apart,  or  5  or  6  feet  for  deep  girders,  they  will  prevent  any 
buckling  of  the  web. 

There  is  no  rational  method  of  determining  the  size  of  these 
stiffeners.    Some  specifications2  give  column  formu- 
las for  this  but  there  is  no  rational  basis  for  it. 
Practice  only  determines  their  size  and  spacing. 

Sometimes  fillers  are  put  under  the  stiffeners, 
between  the  flange  angles,  and  sometimes  the  stiff- 
eners are  "off  set"  or  "crimped"  over  the  flange 
angles  as  shown  in  Fig.  39.  Fillers  should  be  used 
under  stiffeners  bearing  concentrated  loads,  or 
where  there  is  anything  connecting  to  the  girder 
by  means  of  the  stiffener.  Fig>  39< 


1  See  Heller's  "Stresses  in  Structures,"  Art.  73,  page  109. 

Also  see  Johnson's  "Modern  Framed  Structures,"  Art.  130,  page  147. 

2 -See  Cooper's  Specifications  for  'Steel  Railway  Bridges,  1906, 
Art.  47. 

See  also  Spec,  of  the  Am.  Ry.  Eng.  and  M.  of  W.  Assoc.,  1906, 
Art.  77. 


106 


WEB  SPLICES. 


Art.  48. 


Stiffeners  should  be  placed  at  the  ends  of  a  girder,  to  trans- 
mit the  end  reaction  from  the  web,  and  at  all  points  of  concen- 
trated loading.  Stiffeners  should  bear  tightly  against  the  hori- 
zontal legs  of  the  flange  angles  at  all  points  of  concentrated 
loading,  as  the  load  must  be  transmitted  to  the  stiffener  by  direct 
bearing  upon  its  end,  and  from  the  stiffener,  by  means  of  rivets, 
to  the  web. 

The  outstanding  leg  of  the  stiffener  should  not  project  be- 
yond the  edge  of  the  flange  angle,  and  the  other  leg  need  only 
be  large  enough  for  the  rivets. 

48.  Web  Splices.  For  small  girders,  such  as  stringers 
and  floor  beams,  the  web  plates  can  usually  be  obtained  from 

the  mills  in  one  piece, 
and  no  web  splices  are 
necessary.  When,  how- 
ever, the  size  of  the  gir- 
der is  increased,  the 
web  plates  cannot  be 
obtained  in  single 
lengths  and  must  be 
spliced.1 

The  stresses  carried 
by  the  web  at  the  point 
must  be  transferred 
t  h  r  o  u  gh  the  splice 
plates  from  one  web 
plate  to  the  other.  If 
no  bending  moment  is 
regarded  as  being  car- 
ried by  the  web  plate, 
pls-  40*  only  the  shear  has  to  be 

provided  for,  and  the  calculation  of  the  rivets  is  a  very  simple 
matter.  In  this  case  a  splice  similar  to  that  shown  in  Fig.  40 
is  used.  The  rivets  are  usually  not  spaced  over  5  inches  apart, 
and  usually  two  rows  are  used  on  each  side  of  the  splice,  al- 
though this  often  gives  an  excess  of  rivets. 


1For  maximum  sizes  of  plates  which  may  be  obtained,  see  Cambria, 
page  31.    These  limits  vary  considerably  with  different  mills. 


Art.  48  WEB  SPLICES.  107 

Two  splice  plates  should  always  be  used  and  their  combined 
thickness  should  be  greater  than  the  thickness  of  the  web.  A 
pair  of  stiffeners  is  'always  placed  over  the  splice. 

When  a  part  of  the  bending  moment  is  regarded  as  being 
carried  by  the  web,  the  web  splice  must  be  designed  to  provide 
for  this  stress  in  addition  to  the  shear.  The  simplest  form  of 
web  splice  to  calculate,  in  this  case,  is  that  shown  in  Fig.  48, 
in  which  the  plates  FG,  near  the  flanges,  are  assumed  to  take 
care  of  the  bending  moment  in  the  web,  and  the  vertical  plates 
HK,  are  assumed  to  take  all  the  shear.  These  assumptions  give 
an  excess  of  plate  and  of  rivets,  but  a  rigid  calculation  would 
make  a  splice  of  practically  the  same  cost.  See  Art.  52  for  the 
design  of  such  a  splice. 

In  order  that  the  allowed  unit  stress  in  the  flange  proper 
may  not  be  exceeded,  it  is  necessary  to  reduce  the  allowed  unit 
stress  in  the  splice  plates  FG,  in  proportion  to  their  distance 
from  the  neutral  axis.  The  entire  solution  must,  in  any  case,  be 
by  trial. 

The  form  of  splice  shown  in  Fig.  40  may  be  used  in  place 
of  that  of  Fig.  48,  but  the  rivets  must  be  calculated  so  that  the 
resultant  of  the  horizontal  and  vertical  stresses  (due  to  moment 
and  shear)  in  the  outermost  rivets  will  not  exceed  the  allowed 
stress  on  a  rivet.  (12)  This  would  also  be  the  exact  method  of 
calculating  the  rivets  in  Fig.  48.  In  Fig.  40  the  splice  plates 
act  as  a  beam  8'— 7%"  deep  to  carry  the  web  bending  moment, 
and  the  extreme  fiber  stress  in  them  must  not  exceed  the  unit 
stress  in  the  girder  at  an  equal  distance  from  the  neutral  axis. 
If  the  rivets  through  the  web  in  the  outer  rows  have  a  small 
pitch,  one-eighth  of  the  web  area  may  not  be  available  as  flange 
area. 

49.  Flange  Riveting  The  stress  in  the  flange  of  a  girder, 
at  the  end,  is  zero,  and  it  increases  to  a  maximum  somewhere 
between ~the  supports  (for  a  girder  supported  at  the  ends).  The 
increase  of  the  flange  stress  is  due  to  the  addition  of  the  hori- 
zontal shears,1  and  the  rivets  connecting  the  flange  to  the  web, 
at  any  point,  must  be  sufficient  to  transmit  this  horizontal 
increment. 


aSee  Heller's  "Stresses  in  Structures,"  Arts.  17  and  70. 


108 


FLANGE  RIVETING. 


Art.  49. 


Fig.  41  shows  any  part  of  a  girder,  supported  in  any  man- 
ner. M  and  8  are  the  known  moment  and  shear  at  the  section 
AB,  then 

M^=M+S(x-m)-Pl(x-a)-P2(x-b)-PB(x-c) 

Differentiating  with  respect  to  x, -will  give  the  rate  of 

dx 
increase  of  the  moment  along  the  girder. 


*__ 

—b—L  l—F2—J: 


* 


The  flange  stress  at  any  point  is  —-  and,  therefore,  the  rate 

a 

of  increase  of  the  flange  stress 


will  be 


dx 


=- (12) 


[o  o  o  IOOQ  o  o  o  o  o  o  d 

^  l# 


or,  in  words,  the  increase  of 

the    flange    stress    per    inch 

will  be  equal  to  the  shear  at 

the  point  divided  by  the  ef- 

fective depth  of  the  girder  in  3        Fig-  41> 

inches  and  sufficient  rivets  must  be  provided,  connecting  the- 

flanges  to  the  web,  to  transmit  this  increment.    Then,  to  obtain 

the  maximum  permissable  rivet  pitch  in  inches  at  any  point,  the 

value  of  a  rivet  must  be  divided  by  the  increment  per  inch.     (If 

there  is  no  vertical  load  on  the  flange.) 

In  a  girder  whose  cross  section  is  constant  from  end  to  end, 
and  in  whose  design  a  part  of  the  web  has  been  considered  as 
flange  area,  the  pitch  of  the  rivets  may  be  increased  because 
the  part  of  the  flange  stress  which  is  carried  by  the  web  does 
not  have  to  be  transmitted  by  the  rivets.  Since  the  flange 
stresses  are  directly  proportional  to  the  flange  areas,  we  have 
from  equation  (12)  when  one-sixth  of  the  web  is  regarded  as 
flange  area, 


Increment  of  stress  in  flange  proper=—x 


(13) 


or  when  one  eighth  of  the  web  is  regarded  as  flange  area, 


Increment  of  stress  in  flange  proper=~ 

d 


Art.  49  FLANGE  RIVETING.  109 

In  a  girder  with  cover  plates  which  do  not  extend  the  full 
length  of  the  girder,  and  in  whose  design  a  part  of  the  web  has 
been  regarded  as  flange  area,  equation  (13)  or  (14)  may  be  used 
for  that  portion  of  the  girder  at  the  ends,  whose  cross  section  is 
constant,  but  when,  passing  toward  the  middle,  the  first  increase 
in  flange  section  is  made  by  the  addition  of  a  cover  plate,  the 
flange  angles  and  the  part  of  the  web  considered  as  flange  area 
have  already  received  their  maximum  allowed  stress  (See  Fig. 
47)  and,  therefore,  all  of  the  flange  stress  increment  must  go 
into  the  cover  plate  and  enough  rivets  to  transmit  it  must  be 
provided,  both  through  the  angles  and  web,  and  through  the 
cover  plate  and  angles. 

'So  far  we  have  considered  only  the  flange  stress  increments 
as  affecting  the  pitch  of  the  rivets.  If  there  are  any  loads 
resting  upon  the  flange  of  the  girder,  they  must  be  transmitted 
to  the  web,  and  since  the  web  plate  is  not  flush  with  the  backs 
of  the  angles,  the  rivets  in  the  flange  must  perform  this  duty 
unless  the  load  is  carried  directly  by  stiffeners. 

The  top  flange  of  a  deck  plate  girder  is  a  case  of  this  kind, 
and  the  resultant  of  the  two  stresses  (vertical  and  horizontal) 
on  a  rivet  must  not  exceed  the  allowed  rivet  value. 

Usually  only  three  or  four  different  groups  of  rivet  pitches 
are  used  in  the  half  length  of  a  girder.  The  pitch  need  be  fig- 
ured only  at  three  or  four  points  and  then  a  curve  can  be  drawn 
through  these,  which  will  give  the  pitch  at  any  other  point  with 
sufficient  accuracy.  See  Fig.  42  and  Fig.  47. 

The  riveting  in  the  two  flanges  is  always  made  the  same 
when  possible,  although  this  gives  an  excess  in  the  bottom  flange. 

Sometimes  the  pitch  of  rivets  in  the  flange  angles  will  de- 
termine the  width  of  the  vertical  leg  of  the  angles  which  may 
be  used.  For  instance,  if  2Ls  4"x4"  would  answer  for  the  flange 
of  a  stringer,  and  it  was  found  that  the  pitch  of  rivets  required 
was  less  than  the  minimum  allowed  in  a  single  line,  (7)  an 
angle  with  a  vertical  leg  wide  enough  for  two  gage  lines  would 
have  to  be  used. 

Sometimes  the  thickness  of  the  web  plate  will  have  to  be 
increased  over  that  which  would  be  required  to  resist  the  shear, 
in  order  to  provide  sufficient  bearing  area  for  the  flange  rivets, 
so  that  they  will  not  have  to  be  spaced  closer  together  than  the 


110  FLANGE  SPLICES.  Art.  50. 

minimum  allowable  pitch.  Also  the  web  must  be  thick  enough 
so  that  there  is  sufficient  net  area,  horizontally  between  the 
flange  rivets,  to  carry  the  horizontal  increment  of  flange  stress. 
These  considerations  sometimes  make  it  necessary  to  use  a 
thicker  web  plate  at  the  ends  of  a  girder  than  in  the  middle.1 

50  Flange  Splices.  There  are  two  conditions  which  may 
make  it  necessary  to  splice  the  flange  of  a  plate  girder  even  if 
the  girder  is  not  going  to  be  shipped  in  more  than  one  piece. 
Jhese  are, 

1st.  The  flange  angles  may  be  so  heavy  that  they  cannot 
be  obtained  in  one  piece,  of  the  length  required.  (26) 

2nd.  When  the  girder  is  for  a  through  bridge,  frequently 
the  upper  corners  are  rounded,  for  appearance,  and  the  top 
flange  angles  and  one  cover  plate  run  down  the  ends  of  the 
girder.  In  this  case,  the  flange  is  spliced  near  the  ends,  so  that 
the  long  pieces  will  not  have  to  be  handled  in  the  blacksmith 
shop  in  heating,  bending  and  annealing. 

The  flange  splices  should  always  be  made  as  near  the  ends 
as  possible,  where  the  flange  stress  is  least;  and  the  joints  in  the 
component  parts  of  the  flange  should  break  joints.  (29) 

The  splices  are  made  by  means  of  splice  angles  cut  and 
ground  to  fit  the  inside  of  the  flange  angles  and  by  splice  plates 
on  the  top.  The  net  section  of  the  splice  plates  and  angles  does 
not  have  to  equal  the  entire  net  section  of  the  flange  cut,  unless 
the  entire  strength  of  the  cut  portion  is  required  at  the  point  of 
splice.  The  size  of  the  splice  plates  and  angles  and  the  number 
of  rivets  required  are  determined  by  the  proportion  of  the 
actual  stress  at  the  point,  carried  by  the  part  cut. 

To  illustrate  the  application  of  the  principles  set  forth  in 
this  chapter,  the  design  and  methods  of  calculation  for  a  stringer 
and  a  deck  plate  girder  bridge,  will  now  be  given. 

51.  Design  of  a  Stringer.  The  stringer  of  a  railroad 
bridge  is  the  simplest  form  of  plate  girder.  "We  will  assume 
the  following  data: 

Panel  length  27'— 0",  Stringers  6'— 6"  center  to  center, 

Loading  Cooper's  Class  E  40, 


*See  an  article  by  C.  H.  Wood  in  Bng.  News,  Aug.  6.  1908. 


Atr.  61.  DESIGN  OF  A  STRINGER.  Ill 

Specifications  Cooper's  1906  for  Railway  Bridges, 

Material  medium  steel  except  rivets. 

Dead  Load.  The  dead  load  is  estimated  and  consists  of  the 
weight  of  the  floor  (rails,  ties,  guards,  fastenings,  etc.)  and  the 
weight  of  the  stringer  itself.  Except  in  special  cases,  the  weight 
of  the  floor  will  not  exceed  400  pounds  per  lineal  foot  of  track, 
and  the  specifications  §23  will  not  allow  the  use  of  a  lesser 
weight.  The  weight  of  the  stringer  will  be  taken  at  160  pounds 
per  lineal  foot.  This  gives  a  total  dead  load  per  lineal  foot  of 
stringer,  of  360  pounds. 

The  dead  load  moment=  360X^7x27  =  32,800  ft.  Ibs. 

The  live  load  moment  (See  Spec.  Table  I)  =344,600  ft.  Ibs.1 
Depth.  The  depth  of  the  stringer  must  now  be  decided 
upon.  The  economic  depth  may  be  determined  from  equation 
(10),  as  §46  of  the  specifications  directs  that  no  part  of  the  web 
area  may  be  considered  as  flange  area.  The  value  of  st  to  use  in 
the  formula  is  determined  from  §31  of  the  specifications,  and  is 
different  for  live  and  dead  loads.  The  dead  load  moment  may 
be  reduced  to  an  equivalent  live  load  moment,  in  this  ease  by 
dividing  it  by  2,  and  then  the  live  load  unit  stress  may  be  used 
with  the  resultant  total  moment.  This  will  give  a  total  equiva- 
lent moment  of  361,000  ft.  Ibs.  Assuming  the  web  to  be  %" 
thick  we  get 

Cu""~" JL •  O M  **.  I  •  ••   "  <«    — 0  JL>0  IXlCllCS. 

\    10000XM 
If  there  are  no  local  conditions  which  will  limit  the  depth 

of  the  stringer,  such  as  the  height  from  base  of  rail  to  masonry, 
under  clearance  or  depth  of  floor  beam,  we  can  use  a  51"  web 
plate.  This  will  give  an  area  of  web  of  51X%=19.13  sq.  in. 

The  maximum  shear  is  as  follows : 

Live  load  end  shear=59,300  Ibs.  (See  Spec.  Table  I) 

Dead  load  end  shear=  4,900  Ibs. 

Total  Max.  end  shear=64,200  Ibs. 

This  will  give  a  maximum  unit  shear  on  the  web  of  — — —  = 

19 . 13 


3,360  Ibs.  per  sq.  in.,  which  is  safe. 


*For  method  of  calculation   of  maximum   moment  see   Heller's 
"Stresses  in  Structures,"  Art.  134,  page  260. 


112  DESIGN  OF  A  STRINGER.  Art.  51. 

The  depth  back  to  back  of  angles  is  always  made  %"  more 
than  the  depth  of  the  web  plate  (26)  so  that  the  web  will  not 
project  beyond  the  angles  at  any  point.1  An  approximate  effec- 
tive depth  must  now  be  assumed  (45)  for  determining  the  re- 
quired flange.  We  will  take  50.5  inches. 

Flanges.  The  following  are  the  approximate  flange  stresses : 

32800  X 12 

Dead  Load= =  7,800  Ibs. 

50.5 

844600  X  12 

Live  Load  = =81,900  Ibs. 

50.6 

Dividing  these  by  their  respective  unit  stresses  we  get, 

7800 
Approx.  Req.  D.L.  Area= =0.39  sq.  in. 

.20000 
81900 

Approx.  Req.  L.L.  Area= =8 . 19  sq.  in. 

1UUUU 

Approx.  Req.  Total  Net  Area      =8.58  sq.  in. 

2Ls  6"X3y2"Xflr"  gives   2X5.03-2XAX1=8.93   sq.    in. 

Net  (using  %"  rivets). 

The  effective  depth,  using  these  angles  with  the  long  legs 
horizontal,  will  be  51.25—2X0.86=49.53  inches.  This  will  give 
the  following  flange  stresses, 

Dead  Load=  828°°X32    =  8,000  Ibs. 

344600  V  12 

Live   Load= — ^  *      .=83,500  Ibs. 

and  the  required  areas  will  be 

8000 

Dead  Load  Area= =0.40  sq.  in. 

20000 

DOC/VX 

Live  Load  Area^= =8.35  sq.  in. 

Total  Req.  Net  Area=8.75  sq.  in. 


Sometimes  on  stringer®  without  cover  plates,,  the  web  is  made 
to  project  an  inch  above  the  top  flange  angles  and  the  ties  are  notched 
tor  this  instead  of  over  the  entire  flange. 


Art.  61.  DESIGN  OF  A  STRINGER.  113 

It  will  be  found  that  the  flange  section  above  given  is  the 
most  economical  for  this  case.  The  actual  net  area  only  exceeds 
the  required  by  0.19  sq.  in.1 

We  must  now  determine  the  rivet  pitch  in  the  flanges  in 
order  to  see  if  we  can  get  the  required  number  of  rivets  in  a 
single  line  (49)  without  using  a  less  pitch  than  is  allowed. 
(See  Spec.  §54).  (7) 

Flange  Riveting.     Total  Max.  End  Shear=64,200  Ibs. 

The  horizontal  increment  of  flange  stress  from  equation 

64200 

(12)    is =1296  Ibs.  per  lineal  inch.      The  top  flange  also 

49.63 

carries  the  weight  of  the  floor  and  the  live  load  direct,  which 
must  be  transmitted  to  the  web  through  the  flange  rivets.  (49) 
The  dead  load  on  the  top  flange  is  200  Ibs.  per  lineal  foot,  equal 
to  17  Ibs.  per  lineal  inch.  The  maximum  concentrated  live  load 
on  any  point  of  the  stringer  will  be  one  driver  or  20,000  pounds, 
which  may  be  considered  as  distributed  over  three  ties  (See 
Spec.  §15)  spaced  14  inches  center  to  center,  making  the  load 

20000 

per  inch =476  Ibs.    This  makes  the  total  maximum  vertical 

3XH 

load  on  the  top  flange  493  Ibs.  per  lineal  inch.  The  resultant 
of  these  vertical  and  horizontal  stresses=  J  (493  )2+(  1296  )2= 
3387  Ibs.  per  lineal  inch. 

The  value  of  a  rivet  in  bearing  on  the  web  is  3938  pounds. 

(See  Spec.   §40,  floor  system.)      The  maximum  allowed  pitch 

3938 

at  the  ends  then  will  be =  2.83  inches,  which  is  greater  than 

1387 

three  diameters  of  the  rivet  and  is,  therefore,  allowable  in  a 
single  line. 

The  required  pitches  may  be  determined  in  a  similar  man- 
ner at  the  quarter  point  and  center  after  the  shears  at  these 
points  have  been  calculated,  and  when  plotted,  as  in  Fig.  42,  we 
can  scale  the  required  pitch  at  any  point.  The  actual  pitches 
used  should  come  within  the  curve,  as  shown  by  the  stepped  line. 


xln  some  cases,  the  .bottom  laterals  of  the  bridge  are  connected  to 
the  bottom  flanges  of  the  stringers,  in  that  case  the  net  section  i®  re- 
duced by  an  extra  hole  out  of  the  horizontal  leg  of  one  flange  angle. 


114 


DESIGN  OF  A  STRINGER. 


Art.  51. 


Stiffeners.     According  to  the  specifications,  §47,  the  web 

must  be  stiffened  when  the 
shearing  stress  per  square 
inch  exceeds  10000— 75#,  in 
which  H  is  the  ratio  of  the 
depth  of  the  web  to  its  thick- 
ness. By  this  formula,  the 
maximum  allowed  shearing 
Pig.  42.  stress  on  this  web,  without 

stiffeners,  is  a  negative  quan- 
tity, so  stiffeners  must  be  used  throughout  the  length,  spaced 
not  more  than  the  depth  of  the  girder  apart  (Spec.  §47).  We 
will  have  to  put  in  six  pairs  of  intermediate  stiffeners  in  order 
to  keep  within  this  limit. 

The  size  of  the  stiffeners  must  be  determined  by  the  column 
formula  given  in  the  specifications  §48.  The  smallest  angles 
which  can  be  used  with  %"  rivets  have  3"  legs  (Cambria,  page 
54)  and  the  thinnest  metal  allowed  is  %"  thick  (Spec.  §82),  so 
for  the  stiffeners  we  will  try  2Ls  3"X3"X%".  The  radius  of 
gyration  of  the  stiffeners,  fillers  and  enclosed  web,  perpendicular 

tothewebisl.35in.P=10000-45  ^=10000-45  ^=8300  Ibs. 

per  sq.  in.  The  gross  area  of  the  stiffeners,  fillers  and  enclosed 
web  is  8.72  sq.  in.,  therefore,  the  stiffeners  are  good  for  a  shear 
of  8.72X8300=72300  Ibs.,  which  is  greater  than  the  maximum 
shear  in  the  girder. 

The  specifications  §79,  require  that  the  compression 
flanges  of  beams  and  girders  shall  be  stayed  against  transverse 

crippling  when  the 
length  is  more  than 
sixteen  times  the 
width.  In  this  case 
the  top  flanges  may 
have  an  unsupported 
length  of  about  16 
feet.  They  may  be  held  by  means  of  a  cross  frame  at  the  middle, 
making  the  unsupported  length  13%  feet,  or  by  means  of  a 
subdivided  Warren  lateral  system  of  single  angles  between  the 
top  flanges,  as  shown  in  Fig.  43,  making  the  unsupported  length 


Art.  51.  DESIGN  OF  A  STRINGER.  115 

of  the  flange  about  9  feet.  The  size  of  these  angles  may  be 
determined  by  the  minimum  requirements  of  the  specifications 
§§82  and  83.  A  common  size  is  3%"X3"X%". 

If  the  track  is  on  a  curve,  these  angles  must  be  made  large 
enough  to  take  care  of  the  centrifugal  force.1 

Estimate  of  Weight.  An  estimate  of  the  weight  of  the 
stringer  will  now  be  made  to  see  how  it  compares  with  the 
weight  assumed  in  the  dead  load.  (160  Ibs.  per  foot) 

Flanges  4Ls  6"X3%"XA"  @  l1-1          =  68-4  lbs-  Per  foot- 

Web  51"  X%"  =  65.0  lbs.  per  foot, 

Stiffeners  2Ls  3"X3"X%"   (Equivalent)^  22.6  lbs.  per  foot. 

Bracing  IL  3%"X3"X%"   (Equivalent)^    5.0  lbs.  per  foot. 


161.0  lbs.  per  foot. 
Rivets,  say  3%=    4.8  lbs.  per  foot. 

Total=165.8  lbs.  per  foot. 


This  is  near  enough  to  the  weight  assumed  so  that  no  re- 
calculation will  be  necessary. 

In  all  cases  the  assumed  dead  load  should  be  checked  with 
the  final  estimate  to  make  sure  none  of  the  actual  stresses  will 
exceed  those  provided  for  in  the  design,  and  also  to  see  if  any 
excess  of  material  has  been  used  over  that  actually  required. 

No  web  splices  are  necessary,  as  the  web  plates  can  be  ob- 
tained from  the  mills  in  one  piece.  (See  Cambria,  page  31.) 

52.  Design  of  a  Deck  Plate  Girder  Bridge.  The  following 
data  will  be  assumed: 

Span,  103  ft.  Extreme  (100  ft.  c.  to  c.  of  bearings). 

Loading,  Cooper's  Class  E50. 

Specifications,  American  Railway  Engineering  and  Mainte- 
nance of  Way  Assoc.,  1906. 

The  width  center  to  center  of  girders  should  not  be  less 
than  about  -fa  the  span,  and  should  never  be  less  than  six  feet 
for  a  standard  gage  track.  We  will  use  a  width  of  eight  feet 
center  to  center. 

Floor.  The  ties  will  be  made  8  inches  wide,  spaced  with 
six  inch  openings  (Spec.  §5).  The  maximum  driver  load  will 


*See  Heller's  "Stresses  in  Structures,"  Art.  166,  page  307. 


116  DECK  PLATE  GIRDER  BRIDGE.  Art.  52. 

be  that  due  to  the  special  loading  (Spec.  §7)  and  will  be  for 
one  rail—  x— —  =31,200  Ibs.  This  is  assumed  to  be  distributed 

over  three  ties  (Spec.  §5),  making  a  pair  of  loads  of  10,400  Ibs. 
each  on  each  tie,  besides  the  dead  load.  To  this  must  be  added 
100%  of  the  live  load  for  impact  (Spec.  §5)  and  the  dead  load 
t/^  may  be  taken  at  200  Ibs.  at  each  rail 
for  each  tie,  making  a  total  of  21,000 
pounds  at  each  rail.  The  maximum 


-*<•"""-""  •'        moment  on  the  tie  will  be  iy2X 21000= 
Fig-  44.  31,500  ft.  Ibs.   See  Fig.  44.   Substituting 

si 

in  the  formula  M— —  (Equation  3,  Art.  44)  we  can  solve  for 

the  depth  of  the  tie  directly. 

2000X^ 
31500X12= —==-  from  which  d2=141.75     d=11.9" 

The  ties,  therefore,  will  be  8"X12"XH  ft.  long,  spaced 
14"  center  to  center. 

De,ad  Load.  The  weight  of  the  floor  can  now  be  calculated 
(Spec.  §6). 

Ties  8"X12"X11'=396  Ibs.  each?^i?^540  Ibs.  per  lin.  ft.  of  Br. 

Guards  2-6"X8"  8X4y2=  36  Ibs.  per  lin.  ft.  of  Br. 

Rails  and  fastenings  =150  Ibs.  per  lin.  ft.  of  Br. 

Total  weight  of  flooi^=526  Ibs.  per  lin.  ft.  of  Br. 

The  weight  of  the  steel  work  may  be  estimated  by  compari- 
son with  similar  structures,  of  which  the  weights  are  known,  or 
may  be  approximately  determined  from  an  empirical  formula 
of  the  form 

(15) 


In  the  above  formula  "&"  represents  that  part  of  the  metal 
work,  the  weight  of  which  does  not  vary  appreciably  with  a 
change  in  span  length,  and  may  be  taken  at  about  200  Ibs.  in 
the  present  example,  and  "a,"  we  will  assume  as  12.5. 


'See  Heller's  "Stresses  in  Structures,"  Art.  118,  page  219. 

See  also  Johnson's  "Modern  Framed  Structures,"  Art.  62,  page  43. 


Art.  52.  DECK  PLATE  GIRDER  BRIDGE.  117 

The  weight   of  the   steel   work=12.5L+200 

=1450  Ibs.  per  lin.  ft.  of  Br. 
The  weight  of  the  floor,  from  above=i  526  Ibs.  per  lin.  ft.  of  Br. 

Total  dead  load=1976  Ibs.  per  lin.  ft.  of  Br. 

Stresses.      (43)      The   maximum   live   load   moments    and 

shears  should  be  calculated  at  several  points  in  the  girder.  Then 

a  curve  can  be  drawn  through  these  values  when  plotted,  which 

will  represent  the  values  at  all  points  sufficiently  close. 

The  maximum  moment  (near  the  center)  and  maximum 
shear  (at  the  end)  in  the  girder,  should  be  calculated  from  the 
actual  wheel  loads1,  and  then  the  moments  and  shears  at  the 
other  points  may  be  calculated  from  equivalent  uniform  loads2 
derived  from  this  maximum  moment  and  shear. 

The  maximum 

J      moment  will  occur 

twith  wheel  12  near 
the   center  of  the 

FiS-  45-  span  (see  Fig.  45) 

and  the  center  of  gravity  of  all  the  loads  on  the  span  must  be 
as  far  on  one  side  of  the  center  as  wheel  12  is  on  the  other.  Then 
from  Fig.  45  we  can  write  the  following  equations : 


40+z=50—  — 

jj^==Moment  about  A  of  all  loads  to  the  left  of  A,  on  the 
span. 

WA  =Sum  of  all  loads  to  the  left  of  A,  on  the  span. 
w  =Uniform  load  per  lineal  foot. 

Substituting  in  the  above  equations  and  solving  for  e  and  x, 
we  get  6=0.2  ft.  z=9.9  ft. 

Having  determined  the  position  of  the  loads,  the  calculation 
of  the  moment  is  a  simple  matter.  The  work  may  be  greatly 
facilitated  by  the  use  of  a  moment  table  if  one  is  available. 


JSee  Heller's  "Stresses  in  Structures,"  Art.  134,  page  260. 
'See  Heller's  "Stresses  dn  Structures,"  Art.  144,  page  269. 


118  DECK  PLATE  GIKDEK  BRIDGE.  Art.  52. 

The  maximum  live  load  moment  in  the  girder  is  4,025,000 
ft.  Ibs. 

The  maximum  live  load  end  shear  will  occur  with  wheel  2 
at  the  end  of  the  girder,  and  is  187,500  Ibs. 

The  equivalent  uniform  load  for  moments  is  determined  by 

setting  the  maximum  live  load  moment  equal  to  —  —  and  solving 

8 

for  w. 

4,025,000=  2X12229 

w=3220  Ibs.  per  lin.  foot  of  girder. 
The  equivalent  uniform  load  for  shears  is  obtained  by  set- 

ting the  maximum  live  load  end  shear  equal  to   —    and  solving 
for  w. 

187)50o= 

w=3750  Ibs.  per  lin.  foot  of  girder. 

From  these  equivalent  uniform  loads,  the  stress  at  any  point 
can  be  obtained  with  sufficient  accuracy. 

The  uniform  load  moment  varies  as  the  ordinates  of  a  para- 
bola, and  can  be  scaled  from  a  diagram  drawn  as  shown  in 
Fig.  47. 

The  shears  will  now  be  figured  from  the  equivalent  uniform 
load  at  points  16  §  ft.,  33%  ft.,  and  50  ft.  from  the  end, 
(selected  on  account  of  the  location  of  the  web  splices  as  deter- 
mined later.) 

For  location  of  points  A,  B,  C  and  D  see  stress  sheet,  Fig.  53. 


Live  load  shear  at  A=-~  =187,500  Ibs. 

100X2 

Live  load  shear  at  B=  37^°X8^32  =430,200  Ibs. 


Live  load  shear  at  C=  =  83,300  Ibs. 


Live  load  shear  at  D=  =  46,900  Ibs.1 


irFhe  live  load  shear  at  D  calculated  from  the  actual  wiheel  loads 
Is  49,200  Ibs.,  or  4.9%  greater  than  that  given  by  the  equivalent  uni- 
form load. 


Art.  52.  DECK  PLATE  GIRDER  BRIDGE.  119 

To  each  of  the  stresses  thus  far  determined,  must  be  added 
the  impact  stress  as  determined  by  the  formula  given  in  the 

specifications  §9,  1=8  — 

£  +  300 

Summary  of  Stresses. 

Maximum   Live   Load   Moment=4,025,000  ft.  Ibs. 

lmpact=  4026000  X  300  =3)018,800  ft.  Ibs. 

100  +  300 

Dead  Load=1976X8™°2X10°  =1,235,000  ft.  Ibs. 
Total   Maximum   Moment=8,278,800  ft.  Ibs. 
Live  Load  End  Shear=187,500  Ibs. 

Impact=187500X3QO      =140,600  Ibs. 
100  +  300 

Dead  Load=1976X1°°  =  49,400  Ibs. 
Total  End  Shear    =377,500  Ibs. 


Live  Load  Shear  at  5=130,200  Ibs. 

T  130200X300  imn/v\n- 

Impact= — =102.000  Ibs. 

83K  4-  300 
D.L.=49400-y3X49400=32,900  Ibs. 


Total  Shear  at  B  =265,100  Ibs. 
Live  Load  Shear  at  C=  83,300  Ibs. 


D.L.=49400-f  X49400=  16,500  Ibs. 

Total  Shear  at  C  =168,000  Ibs. 

Live  Load  Shear  at  D=  46,900  Ibs. 

Impa^46900*300     =40,200  Ibs. 
50  +  300 

Dead  Load  Shear          =       000  Ibs. 


Total  Shear  at  D  =  87,100  Ibs. 

Depth.    The  economic  depth  (46)  can  now  be  figured  from 
equation  (11),  assuming  the  web  to  be  %  inches  thick. 


16000XK 


120  DECK  PLATE  GIRDER  BRIDGE.  Art.  52. 

The  cost  per  pound  of  plates  increases  very  rapidly  as  the 
width  increases,  after  100  inches  is  passed,  until  at  130  inches 
wide  the  cost  has  reached  about  40%  excess  per  pound  over  the 
cost  of  plates  100  inches  wide  and  less.  Also  it  must  be  remem- 
bered that  pieces  over  about  ten  feet  deep  cannot  be  shipped  on 
many  roads,  (31)  so  we  will  make  the  web  of  the  girder  only 
120  inches  deep,  instead  of  the  depth  given  by  the  formula. 
This  is  probably  more  nearly  the  least  cost  depth,  than  that  given 
by  the  formula,  in  this  case. 

Web.  The  web  plate  will  have  to  take  the  shear  (44)  with- 
out exceeding  a  unit  stress  of  10,000  Ibs.  per  sq.  in.  on  the  gross 

area  (See  specifications  §18).    The  required  area  will  be  37750°. 
37  75  10000 

=37.75  sq.  in.  —  •  —  =0.315  inches  required  thickness,  so  we  can 

use  a  web  plate  120"x%". 

Flanges.  According  to  the  specifications  §27,  one-eighth 
of  the  gross  web  area  may  be  regarded  as  flange  area.  (45). 
For  an  approximate  effective  depth  10  ft.  will  be  assumed.  This 
gives  a  flange  stress  of  827,900  Ibs.  The  approximate  required 

.„  ,      827900      „  „. 
area  will  be  -  =51.74  sq.  in.  net. 

The  following  flange  section  will  be  tried: 

Sq.  in.  gross  Sq.  in.  Net. 

i/8   Web=i/8X45.00=  5.62  5.62 

2Ls  8"X8"X%"     =26.48    26.48—  6XlX%=21-23 
I_20"xy2"  =10.00    10.00—  2X1X%=  9.00 

1—  20"X%"  =10.00    JO.OO—  2X1X%=  9.00 

=  8-75      8.75— 


Total  gross=60.85  Total  net=52.72 

The  net  areas  here  have  been  figured  with  two  rivet  holes 
out  of  the  vertical  legs  of  the  angles  and  one  out  of  each  hori- 
zontal leg.  (11)  To  obtain  this  as  a  minimum  net  area  the 
pitch  of  the  rivets  in  the  cover  plates  must  never  be  less  than 
about  2%  inches. 

The  location  of  the  center  of  gravity  of  this  flange  is  0.74 
inches  from  the  backs  of  the  angles  as  shown  in  Fig.  46,  making 
the  actual  effective  depth  120.25—2X0.74=118.77  inches. 


Art. 


DECK  PLATE  GIRDER  BRIDGE. 


121 


The  actual  flange  stress  then  is8278800X]2 

118.77 

=836,500  Ibs.,  making  the  required  area= 
=52.28  sq.  in.,  so  the  above  flange 

section  will  answer. 

Length  of  Flange  Plates.  The  required 

lengths  of  the  flange  plates  may  be  calcu- 
Fig.  46.  lated  from  the  equation  of  the  parabola,  in 

this  case,  as  we  are  using  the  equivalent 

uniform  load  for  the  moments.  Or  the 
lengths  may  be  determined  graphically  by  drawing  the  parabola, 
as  shown  in  the  upper  diagram  of  Fig.  47.  The  graphic  method 
is  nearly  always  used,  as  the  moment  diagram  is  frequently  not 
a  simple  curve. 


Fig.  47. 


As  the  moments  and  required  flange  areas  are  directly  pro- 
portional, (when  the  effective  depth  is  constant)  the  areas  will 
vary  as  the  ordinates  of  a  parabola  also,  and  it  is  simpler  to  lay 
off  areas  as  ordinates  instead  of  moments.  Any  convenient 
scales  may  be  chosen  for  lengths  and  areas.  In  this  case  the 


122  DECK  PLATE  GIRDER  BRIDGE.  Art.  62. 

middle  ordinate  of  the  parabola  is  52.28  (=Reqd.  net  flange 
area)  and  the  curve  may  be  drawn  in  any  one  of  several  ways, 
the  method  shown  is  a  simple  one. 

After  the  curve  of  required  areas  is  drawn  in,  the  net  areas 
of  the  component  parts  of  the  flange  are  measured  off  on  the 
center  line  and  horizontal  lines  through  these  points  represent 
the  parts.  The  required  lengths  of  the  various  pieces  may  now 
be  scaled  off  directly.  The  flange  plates  are  made  2  or  3  feet 
longer  than  the  theoretic  length  in  order  to  provide  a  few  rivets 
through  the  plate  near  the  ends  so  that  the  strength  may  begin 
to  be  effective  where  it  is  required,  and  also  to  compensate  for 
the  fact  that  the  actual  wheel  loads  give  slightly  larger  moments 
near  the  ends  than  the  equivalent  uniform  load.  The  effective 
depth  decreases  a  little  toward  the  ends,  owing  to  the  omission 
of  the  flange  plates,  and  this  will  also  make  the  flange  stress  a 
little  greater  there  than  is  given  by  the  parabola. 

For  a  symmetrical  girder,  only  one  half  the  diagram  need 
be  drawn. 

The  top  flange  plate  next  to  the  angles  is  nearly  always  run 
the  full  length  of  the  girder,  to  cover  the  flange  angles  and  to 
stiffen  them  near  the  ends,  against  the  deflection  of  the  ties. 
(See  specifications  §76.) 

Scaling  from  the  diagram,  Fig.  47,  the  following  are  the  re- 
quired lengths  of  the  flange  plates : 

20"X1/2"— 70  ft.  use  74  ft. 
20"X1/2"-56  ft.  use  60  ft. 
20"XA"— 38  ft-  use  42  ft. 

Flange  Riveting.  (49).  The  horizontal  increment  of  flange 
stress  at  A  (See  Fig.  53)  may  be  determined  from  equation  (14). 
As  the  top  flange  also  carries  the  direct  load  of  the  floor  and 
live  load  the  required  pitch  will  be  less  for  it  than  for  the  bot- 
tom flange,  so  the  bottom  flange  pitch  need  not  be  figured. 

Horizontal  increment=?^X  —  =2812  Ibs.  per  lin.  in. 

116.31      42.10 

The  gross  areas  are  used  for  proportioning  the  stress.  Note 
also  that  the  effective  depth  here  is  less  than  at  the  middle  of 
the  girder. 

The  vertical  load  from  the  floor  is  263  Ibs.  per  lineal  foot 
and  the  weight  of  the  flange  of  the  girder  here  is  127  Ibs.  per 


Art.  62.  DECK  PLATE  GIRDER  BRIDGE.  123 

lineal  foot,  making  a  total  dead  load  of 

390  Ibs.  per  lineal  f  oot=    33  Ibs.  per  lin.  in. 


Live  load  (See  Spec.  §§  5  and  29)=~=  595  Ibs.  per  lin.  in. 

Impact  (See  Spec.  §5)=100%  =  595  Ibs.  per  lin.  in. 

Totat  vertical  load=1223  Ibs.  per  lin.  in. 

The  total  resultant  stress  on  the  rivets  will  be 
I/  (28i2)2+(  I223p=3066  Ibs.  per  lineal  inch. 


Required  rivet  pitch=  -  =2.57  inches. 

To  find  the  horizontal  increment  of  flange  stress  at  B,  we 
must  use  equation  (12)  because  the  web  is  here  carrying  all  the 
bending  stress  allowed,  and  all  of  the  increment  goes  into  the 
flanges  proper. 

Horizontal  increment  =  —  -  —  =2266  Ibs.  per  lineal  inch. 

Vertical  load  (same  as  before)  =1223  Ibs.  per  lineal  inch. 
Resultant  Stress=j/  12232+  22662=2575  Ibs.  per  lineal  inch. 

Required  rivet  pitch=  --  =3.06  inches. 
2575 


Horiz.  increment  at  C=  -  =1415  Ibs.  per  lineal  inch. 

118.77 

Resultant  Stress=j/  12232H-14152=1870  Ibs.  per  lineal  inch. 

787ft 

Required  rivet  pitch=  -  =4.21  inches. 
1870 

Horiz  increment  at  Z>=  --  =  733  Ibs.  per  lineal  inch. 

118.77 

Resultant  Stress=  y  12232  -f-  7332=1426  Ibs.  per  lineal  inch. 


Required  rivet  pitch=  -  =5.52  inches. 

These  rivet  pitches  are  plotted  as  shown  in  Fig.  47  and  the 
actual  pitches  used  are  made  to  come  within  the  curve  as  shown 
by  the  stepped  line. 

The  required  pitch  of  rivets  through  the  flange  plates  is 
determined  by  the  horizontal  increment  of  flange  stress  alone. 
The  total  shear,  at  the  theoretical  end  of  the  first  flange  plate  is 

27ROOO 

276,000  Ibs.    This  gives  a  horizontal  increment  of  -  -  =2360 


124  DECK  PLATE  GIRDER  BRIDGE.  Art.  52. 


Ibs.  per  lineal  inch  and  a  required  rivet  pitch  of  --  —=6.1 

2360 

inches.  As  the  maximum  allowed  pitch  is  6  inches  (See  specifi- 
cations §37)  it  will  not  be  necessary  to  calculate  the  pitch  at 
any  other  points.  The  pitch  of  the  rivets  in  the  cover  plates 
must  bear  some  relation  to  that  of  the  rivets  through  the  verti- 
cal legs  of  the  flange  angles  so  that  they  will  not  interfere.  (29) 

Flange  Splices.  (50).  About  the  maximum  length  of 
angle  8"x8"xy8"  which  can  be  obtained  in  one  piece  is  ninety 
feet,  therefore  the  flange  angles  will  have  to  be  spliced.  We 
will  splice  one  angle  of  each  flange  about  25  feet  from  each  end 
of  the  girder  so  that  both  angles  of  one  flange  will  not  be  cut 
at  the  same  point. 

At  this  point  the  flange  angles  are  carrying  the  maximum 
allowed  stress,  and  the  total  stress  in  one  angle  will  be 
10.61X16,000=169,800  Ibs. 

To  take  this  stress  we  will  use  a  splice  angle  on  the  inside 
of  the  angle  spliced  and  a  plate  inside  of  the  other  angle.  The 
splicing  material  required,  then,  will  be  IL  8"x8"x  f^"  cut  down 
to  7"x7"x«  H"and  ground  to  fit  the  fillet  of  the  flange  angle  and 
one  plate  7"x-f  £-"  These  will  have  an  available  net  area  of  10.53 
sq.  in.  The  length  of  the  angles  will  have  to  be  sufficient  to  take 
enough  rivets  to  transmit  169,800  Ibs.,  and  one-third  of  this  must 
be  transmitted  to  the  plate  on  the  side  opposite  the  angle  cut. 
According  to  the  specifications  §55,  the  rivets  connecting  this 
plate  must  be  increased  66  %%  over  the  number  required  by 
§18  for  the  angle  in  contact  with  the  cut  member. 

169800 

Stress  in  one  leg  of  splice  angle=  -  =56,600  Ibs. 

3 

56600 
Rivets  required  in  angle  on  side  next  to  spliee=          =7.85 

7218 

66%%         =5.25 


Rivets  required  in  angle  on  opposite  side  =13.1 

The  rivet  pitch  at  the  splice  may  be  made  3  inches,  which 
gives  us  a  splice  plate  6*/2  ft.  long  on  the  side  opposite  the  splice 
and  an  angle  4  ft.  long  on  the  side  next  to  the  splice. 

Stiff eners.  (47).  The  stiffeners  must  be  proportioned  ac- 
cording to  specifications  §§16  and  77.  The  end  shear  which 
must  be  transmitted  by  the  end  stiffeners  to  the  abutment  is 


Art.  52.  DECK  PLATE  GIRDER  BRIDGE.  126 


377,500  Ibs.    To  take  this  load  we  will  need  +50%=72 

7876 

rivets.     (See  Spec.  §  56.) 

This  number  can  be  put  into  three  pairs  of  stiffener  angles 
with  a  single  line  of  rivets  in  each  angle.    The  stress,  then,  on 


each  pair  of  angles  wiU  be,  =125,800  Ibs.    The  outstand- 

3 

ing  legs  of  these  end  stiffeners  must  be  as  wide  as  the  flange 
angles  will  allow,  so  we  will  try  for  these  2Ls  7"x3y2"xi/2". 

Ml 

The  allowed  unit  stress  is  16000—70  --=15000  Ibs.  per  sq.  in. 

4.24 

The  required  area  of  one  pair  of  angles=  -  =8.39  sq.  in. 

16000 

We  can,  therefore,  use  for  these  stiffeners,  2Ls  7"x3%"xTV" 
whose  area  is  8.82  sq.  in. 

The  minimum  size  of  angles  allowed  for  the  intermediate 

stiffeners  is  --  1-2=6  inches  for  the  outstanding  leg.  (See  Spec. 
30 

§  77).    We  will  use  for  these  2Ls  6"x3y2"x3/8". 

The  spacing  of  the  intermediate  stiffeners  must  not  exceed 
the  distance  "d"  allowed  by  the  formula  in  §77  of  the  specifi- 
cations. 


Required  spacing  -at  A=^-(  12000  -2^29  V=34  inches. 

40  \  46    / 

Eequired  spacing  at  B=  —  (12000  --  )=57  inches. 

820\  46    / 

Required  spacing  at  0=—  M2000  —  -  \=77f  inches. 
Required  spacing  at  D=—  M2000—  —  —  )=94  inches. 

Web  Splices.  (48).  The  total  length  of  the  girder  is  103  ft. 
Plates  12Q  inches  in  width  and  only  %  inches  thick  are  not  listed 
in  the  Cambria  hand  book,  but  in  the  Carnegie  shape  book  they 
are  given  and  can  be  obtained  up  to  220  inches  long,  or  18'  —  4". 
It  will  therefore  be  necessary  to  splice  the  web  at  five  points, 
making  it  in  six  pieces.  The  end  sections  may  be  made  18'—  2" 
long  and  the  intermediate  sections  each  16'—  8".  This  will  make 
the  spacing  of  the  cross  frames  uniform. 

The  maximum  bending  moment  at  the  first  splice  B,  is  as 
follows  : 


126 


DECK  PLATE  GIRDER  BRIDGE. 


Art.  62. 


Dead  Load=  686000  ft.  Ibs. 
Live  Load  =2236000  ft.  Ibs. 
Impact  =1677000  ft.  Ibs. 

Total=4599000  ft.  Ibs. 

The  actual  flange  area  effective  at  this  point  is  35.84  sq.  in., 
and  therefore  the  bending  moment  taken  by  the  web  here  is 

K    on 

l^f.  X  4,599,000=721,000  ft.  Ibs.     At  the  splice  this  moment 

OO.OTC 

must  be  resisted  by  the  splice  plates  FG,  and  the  stress  in  these 
plates  due  to  the  moment  will  be  721Q09°2X12  =94,000  Ibs. 

The  maximum  allowed  unit  stress  on  the  extreme  fiber  of 
the  girder  is  16,000  Ibs.  per  sq.  in.,  and  the  maximum  allowed 
unit  stress  on  the  splice  plates  FG  will  be  proportional  to  their 
distances  from  the  neutral  axis  of  the  girder,  or, 

—  X  16,000=12,145  Ibs.  per  sq.  in. 
606 

94000 
and  the  required  area  in  the  splice  plates  will  be--— -=7.73 

sq.  in. 

This  will  require  2  plates  12"x%"  (net  area^=12.00— 4X 
2XlXy2=8.00  sq.  in.). 

The  number  of 
rivets  on  each  side  of 
the  splice  in  these 

.   .  .,,    ,        94000 

plates   will  be    7876 

=  12. 

The  vertical 
splice  plates  to  take 
the  shear  will  require 

?5™2  =34  rivets  on 

7876 

each  side.  The  de- 
sign shown  in  Fig.  48 
has  36  rivets  on  each 
side. 

These  figures  are 
for  the  splice  at  B, 
but  usually  the  same 
design  is  used  for  all 
the  splices. 


Fig.  48. 


Art.  52.  DECK  PLATE  GIRDER  BRIDGE.  127 

It  will  be  noted  that  the  maximum  shear  and  maximum 
moment  have  been  used  here  as  occurring  simultaneously.  This 
is  on  the  side  of  safety,  but  a  rigid  solution  would  not  give  a 
splice  appreciably  smaller. 

A  splice  similar  to  the  one  shown  in  Fig.  40  may  be  used 
and  calculated  as  follows.  Here  the  number  of  rivets  must  first 
be  assumed  and  then  the  stress  in  them  calculated,  to  see  that  it 
does  not  exceed  the  allowed  units. 

The  splice,  as  drawn  in  Fig.  40,  contains  52  rivets  on  each 

O£?c  i  A/\ 

side,  the  vertical  stress  on  each  rivet,  due  to  shear,  is  -       -  =• 

52 

5,100  Ibs.  The  bending  moment  to  be  resisted  by  these  rivets  is 
721,000X12=8,652,000  inch  pounds.  The  amount  of  stress 
on  each  rivet  due  to  bending  moment  will  be  in  direct  propor- 
tion to  its  distance  from  the  neutral  axis.  (12) 

Calling  the  stress  on  the  outermost  rivet  S,  we  have: 

4#X50+4#X  |J-X46+4SX||-X42-|-...  =8,652,000,  or  using 

the  letter  y  to  represent  the  distance  from  the  neutral  axis  to 
the  rivet,  in  each  case,  we  have:1 


In  this  case  22/2=ll,700  and  #=  =9,243  Ibs. 


The  resultant  maximum  stress  on  the  outer  rivet  is 
I/  51002  -f  924S2  =10,560  Ibs.,  which  is  in  excess  of  the  allowed 
unit,  (7876),  and  therefore  the  number  of  rivets  would  have  to 
be  increased  if  this  type  of  splice  were  used  in  this  girder. 

The  splice  plates  must  be  strong  enough,  when  considered 
as  a  beam  1031/2  inches  deep,  to  carry  the  web's  proportion  of 
the  bending  moment  without  exceeding  a  unit  stress  at  the  top 
and  bottom,  proportional  to  the  distance  from  the  neutral  axis, 

or  -^r^-X  16,000=13,680  Ibs.  in  this  case.   In  figuring  the  mo- 
60 .6 

ment  of  inertia  of  the  plates,  the  rivet  holes  should  be  deducted. 
Lateral  Bracing.2    To  provide  for  wind  stresses  and  vibra- 

^trictly,  these  forces  are  perpendicular  to  lines  drawn  from  the 
center  of  gravity  of  the  entire  group  of  rivets,  to  each  rivet. 
*See  Heller's  "Stresses  in  Structures,"  Chapter  XIV. 


128  DECK  PLATE  GIRDER  BRIDGE.  Art.  52, 

tkms  (See  Spec.  §10)  a  lateral  system  must  be  put  in  the  span. 
Sometimes  two  systems  are  used,  one  in  the  plane  of  each  flange, 
and  sometimes  only  one  is  used,  in  the  plane  of  the  top  flange, 
and  the  forces  from  the  lower  flange  are  transferred  to  the 
upper  system  by  means  of  cross-frames  (See  Fig.  51)  at  inter- 
vals. Cross-frames  are  also  put  in  to  stiffen  the  bridge,  when 
two  systems  of  laterals  are  used.  They  are  usually  placed  from 
15  to  20  feet  apart,  depending  upon  the  width  of  the  flanges 
of  the  girders. 

In  a  deck  plate  girder  bridge,  the  lateral  system  is  of  the 
Warren,  or  sub-divided  Warren  type  of  truss  with  an  even 
number  of  panels,  so  as  to  be  symmetrical  about  the  center  line. 
The  number  of  panels  is  so  chosen  that  the  laterals  will  be 
efficient,  that  is,  so  that  they  will  not  be  inclined  at  too  great 
an  angle  with  the  direction  of  the  wind.  Also,  the  panels  must 
be  short  enough  so  that  the  actual  unit  stress  in  the  top  flange 
of  the  girder  will  not  exceed  that  allowed  by  the  specifications 
28. 


v 

The  actual  unit  stress  in  the  top  flange  is  22^= 

60.86 

Ibs.  per  sq.  in.     Equating  this  to  the  unit  as  given  in  §28  and 
solving  for  I,  we  get  13,750=16,000—  200^=16,000—  10Z  from 

which  102=2,250  and  Z=225  in<jhes=18'9". 

The  unsupported  length  of  the  top  flange  must  not  exceed 
this  amount. 

We  will  divide  the  span  into  12  panels,  using  a  single 
system  in  the  plane  of  the  top  flange,  and  put  in  cross  frames 
at  every  second  panel  point.  This  will  make  a  cross  frame  fall 
at  each  web  splice.  This  is  not  necessary,  but  a  stiff  ener  must 
be  at  each  cross  frame. 

As  but  one  system  of  laterals  is  to  be  used,  it  must  be 
proportioned  to  carry  the  entire  lateral  force.1  From  the  speci- 
fication §10  the  load  is  200+200+10%  of  5000=900  Ibs.  per 
lineal  foot  of  girder,  and  all  of  this  is  to  be  considered  as  a 
moving  load. 


1FV>r  the  calculation  of  the  stresses  in  lateral  systems  of  bridges 
having  curved  track  see  Heller's  "Stresses  in  Structures,"  Art.  166, 
page  304. 


Art.  62. 


DECK  PLATE  GIRDER  BRIDGE. 


129 


The  stresses  in  the  laterals  will  be  alternately  compression 
and  tension,  and  will  all  reverse  when  the  direction  of  the  wind 
reverses.  Laterals,  however,  are  never  designed  for  reversals  of 
stress,  (See  Spec.  §20)  so  far  as  the  reversal  of  the  wind  is 
concerned,  because  such  reversals  would  occur  only  at  long 
intervals. 

Since  it  requires  more  material  to  take  care  of  the  com- 
pression than  the  tension  in  a  lateral,  we  are  concerned  only 
with  the  compressive  stresses,  and  choose  that  direction  of  the 
wind  which,  for  any  particular  lateral,  will  give  compression 
in  it.-  It  will  be  assumed  that  the  load  is  all  applied  at  the 
windward  panel  points,  although  the  live  load  is  really  applied 
at  both  girders.  This  assumption  is  on  the  safe  side,  and  simpli- 
fies the  calculation  of  stresses. 

On  account  of  the  cross  frames,  there  are  12  panels  on  one 
side  and  six  on  the  other.  When  the  wind  is  blowing  as  indi- 
cated in  Fig.  49,  all  of  the  panel  loads  will  be  equal  and  are 
16.67X900=15,000  Ibs.  each.  This  direction  of  the  wind  will 
give  maximum  compressive  stresses  in  BC,  DE,  and  FG,  and 
these  will  be  as  follows : 


29  7 


When  the  wind  blows  in  the  other  direction  as  shown  in 
Fig.  50,  the  compressive  stresses  will  occur  in  AB,  CD  and  EF. 
The  panel  loads  on  the  lateral  system  for  full  loading  are  shown. 


130  DECK  PLATE  GIRDER  BRIDGE.  Art.  52. 


Ibs. 
Ibs. 
#^=16,950X^.0=24,500  Ibs. 

According  to  the  specification  §23,  the  unit  stress  for  later- 
als may  be  increased  25%  over  that  given  for  -other  members, 
and  according  to  §72  the  smallest  angle  allowed  is  3%"x3"x%". 
It  is  usual,  where  possible,  to  make  laterals  of  single  angles. 
The  least  radius  of  gyration  of  a  single  angle  3%"x3"x%"  is 
0.62".  The  unsupported  length  may  be  taken  as  the  length 
between  edges  of  flange  angles,  and  in  this  case  will  be  about 
11.55-1.55=10.0  ft.=120  inches. 

16,000—  70  ^  =2,450  Ibs.  per  sq.  in.  Adding  25%  gives 
3,060  Ibs.  per  sq.  in.  This  makes  IL  3y2"x3"x3/8"  worth 
2.30X3,060=7,040  Ibs.,  which  is  far  less  than  the  least  stress 
in  the  lateral  system. 

Trying  IL  4"x4",  the  least  radius  of  gyration  is  0.79"  and 
the  allowed  unit  stress  is  6710.  The  required  area  for 


Use  for  FG  !L4"x4"x  A  "•    Actual  area=3.31  sq.  in. 

24^00 

Using  a  4"x4"  .angle  for  EF  would  require—  —  =3.66  sq. 

6710 

in.  This  would  require  lL4"x4"x%"  which  weighs  more  than 
!L5"x5"x3/8",  so  we  will  try  !L5"x5".  The  least  radius  of 
gyration=0.98"  and  the  allowed  unit  stress  in  9,300  Ibs.  per 


sq.  in.    The  required  area  for  EF=-=2M  sq.  in. 

9300 

Use  for  EF  !L5"x5"x%".    Actual  area^=3.61  sq.  in. 


Using  a  5"x5"  angle  for  DE  requires          -  =3.89  sq.  in. 

9300 


Use  for  DE  lIS'^'x^".    Actual  area=4.19  eq.  in. 

SflfiOO 

Using  a  5r/x5r/  angle  for  CD  requires  -  =4.26  sq.  in.,  so 

9300 

we  will  try  !L6"x6".    The  least  radius  of  gyration  is  1.18"  and 
the  allowed  unit  stress  is  11,110  Ibs.  per  sq.  in.     The  required 

area  for  CJ>=-^L=3.56  sq.  in.     Use  for  CD  lL6"6"x3/8", 
Actual  area=4.36  sq.  in. 


Art.  52. 


DECK  PLATE  GIRDER  BRIDGE. 

64100 


131 


Required  area  for  BC= 

Actual  area=5.06  sq.  in. 


.87  sq.  in.     Use  for  BC 


!L6"x6"x  T 


68500 


=5.27  sq.  in.     Use  for  AB 


Required  area  for  AB= 
!L6"x6"xy2".    Actual  area=5.75  sq.  in. 

The  end  cross  frames  must  be  proportioned  to  carry  all  the 
wind  load  to  the  abutment.  It  is  usually  considered  that  half 
of  this  goes  through  each  diagonal  to  the  supports,  one  diagonal 
being  in  tension  and  the  other  in  compression. 

The  total  force  acting  at 
the  top  of  the  cross  frame  at 
A  (See  Fig.  49)  is  43,300  Ibs. 

12  8 

Sec.0=* .      Stress    in   top 

8 
strut=21,700  Ibs. 

'Stress  in  diagonal= 
21,700*ec£=34,600  Ibs.  The 
diagonal  in  compression  is 
supported  at  the  middle  in 
one  direction  by  the  tension 
diagonal,  so  an  'angle  having 
Flg*  51*  unequal  legs  will  be  more 

economical    than     an     equal  legged  angle  for  the  diagonals. 

Try  l£6"x3y2"x3/8".  Allowed  unit  stress  is  16000-70— 

1 .94 


[+25%=13,240  Ibs.  per  sq.  in. 


Required  area= 


13240 


5.62  sq.  in.  Actual  <area=3.43  sq.  in. 


As  this  is  larger  than  necessary  we  will  try  !L5"x3%"x%". 
The  allowed  unit  stress  is  11,800  Ibs.  per  sq.  in.    Required  area 

*?4fiOO 

=          =2.93  sq.  in.  Actual  area=3.05  sq.  in.     Use  for  diago- 
nals lL5"x3i/2"x3/8". 

For  the  top  strut  try  l£3y2"x3i/2"x3/8".     Allowed  unit 

21700 

stress=9,000  Ibs.  per  sq.  in.  Required  area= — —  =2.41  sq.  in. 

9000 

Actual  area=2.49  sq.  in.    'This  is  large  enough  so  use  for  top 
and  bottom  struts  LL3y2"x3y2"x3/8". 


132  DECK  PLATE  GIRDER  BRIDGE.  Art.  52 

The  amount  of  load  transferred  by  the  intermediate  cross 
frames  is  only  3,333  Ibs.,  so  the  smallest  angle  allowed  by  the 
specifications  will  be  sufficient.  Use  for  the  intermediate  cross 
frames  3y2"x3"x%"  angles. 

The  number  of  rivets  in  the  end  connections  of  the  lateral 
members  is  determined  by  the  single  shear  value  of  a  rivet.  The 
laterals  will  be  field  riveted,  so  the  value  of  a  rivet  will  be 
6,013  Ibs. 

1AB  requires  ^^-  =10   rivets.     DE  requires  J5M  =6  rivets. 
6013  6013 

BC  requires  -^5.  ==  9   rivets.     EF   requires  ^^.=5   rivets. 
6013  6013 

CD   requires  2^  =  1   rivets.     FG  requires  -?^^4  rivets. 
6013  6013 

^4600 

End  cross  frame  struts  require        -  =5  rivets.   (Shop)' 

21700 

End  cross  frame  diagonals  require—  ——=3  rivets.   (Shop) 

7216 

The  intermediate  cross  frames  will  have  to  have  all  con- 
nections made  with  3  rivets  each,  to  comply  with  the  specifica- 
tions §72. 

Shoes.  The  shoe  should  be  of  such  design  that  it  will  dis- 
tribute the  end  reaction  evenly  over  the  masonry.  For  short 
spans  it  is  customary  to  simply  rivet  a  pkite,  not  less  than  % 
inches  thick,  under  the  end  of  the  girder,  and  allow  this  to  rest 
on  another  similar  plate  resting  on  the  masonry.  With  this 
form  of  shoe  the  load  is  applied  heaviest  at  the  inner  edge  of 
the  masonry  plate  on  -account  of  the  deflection  of  the  girder. 
The  best  results  are  obtained,  especially  for  long  spans,  by  using 
hinged  bolsters.  (See  Spec.  §61.) 

The  required  bearing  on  the  masonry  ('assuming  sandstone) 

is  ^22  ^944  sq.  in.    (See  Spec.  §19).    Using  a  shoe  3  ft.  long, 

400 

Q44 

it  will  require  --  =26.2  inches  width. 
36 

The   smallest    rollers    allowed    are    6    inches    in    diameter 


(Spec.  §58  and  §60)  and  it  will  require  -   =105  lineal 

3600 

inches  of  rollers  under  each  bearing.     (See  Spec.   §19).     This 
will  require  five  rollers  each  21  inches  long. 


Art.  62. 


DECK  PLATE  GIRDER  BRIDGE. 


133 


The  pin  must  be  large  enough  to  properly  transmit  the 

377500 


shear,  .and  the  required  area  is 


=15.7  sq.  in.   This  re- 


2  X  12000 
quires  a  pin  4%  inches  in  diameter. 

The  shoe  must  be  strong  enough  to  distribute  the  end  reac- 
tion, as  a  beam,  from  the  pin,  evenly  over  the  masonry,  and 
must  also  be  strong  enough  laterally  to  transmit  the  wind  forces 
to  the  abutments. 

Fig.  52  shows  a  good  design  for  the  shoe. 

The  estimate  of  weight  can  now  be  made  upon  forms  <as 
described  in  Art.  19,  and  if  the  actual  dead  load  taken  from 
the  estimate  does  not  differ  enough  from  the  assumed  dead  load 
to  cause  a  change  in  the  size  of  any  of  the  members,  the  stress 
sheet  may  be  drawn,  as  shown  in  Fig.  53. 


Fig.  62. 


THE  OHIO  STATE   BRIDGE  COMPANY 

SbWt  Mo.  -'/  -  -  Made  by_  _CZ2£  -----  Date  _  &-&- 

Estim.fr  fQr-^/f 


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Roadway 

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Capacity  Trusses  _ 

Capacity  Floor^S^i^PCC 

Specifications/J»7./^V.£A-A?'/)!£«<: 


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Panels  at  - 
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DL  per  ft.  f    (  Floor  &  Track  _ 
Total 

Panel  Load  per  Truss  Dl 

• LI 


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Total  Lumber  ____ 

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THE   OHIO   STATE    BRIDGE   COMPANY 


Sheet  No._<£  __ 
Estimate  for.  J* 


Date_  Z/^/0^ 


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Art.  53.  THKOUGH  PLATE  GIRDERS.  137 

The  difference  in  the  actual  dead  load  from  that  assumed 
is  1450—1367=83  Ibs.  per  lin.  foot.  This  would  decrease  the 

QQX/1  Q()2 

maximum  moment  -^—-—51,900     ft.  Ibs.,  which  would  de- 
o  X  « 

crease  the  required  flange  area  at  the  center — =0.33 

118.77X16000 

sq.  in.,  making  the  total  required  area  52.28—0.33=51.95  eq.  in. 
If  one  of  the  cover  plates  be  reduced  in  thickness  TV  inches,  the 
actual  net  area  would  be  51.59  sq.  in.,  so  therefore,  the  reduction 
in  dead  load  would  not  allow  a  reduction  in  section  of  any 
member. 

The  stress  sheet  will  now  be  drawn  up.     (See  Fig.  53.) 

53.  Through  Plate  Girders.  In  a  through  plate  girder 
bridge,  all  of  the  live  and  dead  load,  except  the  weight  of  the 
girders  themselves,  is  concentrated  at  the  panel  points;  and  the 
weight  of  the  girders  may  also  be  considered  concentrated  at  the 
panel  points  to  simplify  the  calculations. 

The  shears  and  moments  are  found,  then,  as  for  a  truss 
bridge.1 

The  flange  diagram  (similar  to  Fig.  47)  will  be  polygonal, 
the  area  required  at  each  panel  point  being  calculated. 

The  load  on  the  masonry  will  equal  the  end  shear  of  the 
girder  plus  the  corresponding  end  reaction  of  the  end  floor 
beam  (if  an  end  beam  is  used). 

There  is  no  vertical  load  on  the  flange  rivets,  and  the  pitch 
of  the  rivets  will  be  constant  between  panel  points  'because  the 
shear  is  constant. 

There  can  be  but  one  lateral  system2,  and  this  is  made  of 
the  Pratt  type  with  two  diagonals  in  each  panel.  It  is  assumed 
that  these  diagonals  take  tensile  stresses  only ;  they  are  connected 
to  the  lower  flanges  of  the  stringers  so  as  to  take  up  the  longitudi- 
nal force  due  to  the  application  of  the  brakes  on  a  moving  train. 
This  tractive  stress  would,  otherwise,  produce  sidewise  bending 
in  the  floor  beams. 

The  top  flanges  of  the  girders  are  supported  at  the  panel 
points  by  means  of  solid  web  brackets  extending  down  to  the 


'See  Heller's  "Stresses  in  Structures,"  Chapters  XII  and  XIII. 
'See  Heller's  "Stresses  in  iStructurs,"  Art.  151,  page  275. 


138  THROUGH  PLATE  GIRDERS.  Art.  53. 

top  of  the  floor  beams,  -and  made  as  wide  as  the  specified  clear- 
ance will  allow. 

Sometimes  through  plate  girder  bridges  have  solid  floors, 
in  which  case  the  moment  and  shear  vary  as  for  a  deck  plate 
girder. 

In  this  case  no  lateral  system  would  be  necessary. 


CHAPTER  VI. 
PIN  CONNECTED  BRIDGES. 

54.  Construction.      In  a  truss  bridge,  the  loads  are  de- 
livered to  the  trusses  at  the  panel  points  only.    In  the  ordinary 
bridge  this  is  done  by  means  of  floor  beams  and  stringers.    The 
stringers  carry  the  ties  and  rails  direct,  and  are  in  turn  sup- 
ported by  the  floor  beams  at  the  panel  points  of  the  truss.    This 
construction  causes  the  moment  in  the  truss  to  vary  uniformly 
between  panel  points  and  the  shear  to  be  uniform  in  each  panel. 
(53) 

55.  Types  of  Trusses.      Pin  connected  trusses  are  nearly 
always  of  the  Pratt  or  Baltimore  type,  because  the  pin  connec- 
tion is  not  well  adapted  to  members  whose  stresses  alternate  in 
direction. 

The  tendency  is  toward  long  panels,  that  is,  ordinarily  from 
20  ft.  to  25  ft.,  because  this  gives  few  and  heavy  members  both 
in  the  trusses  >and  in  the  floor  system,  and  these  are  cheaper  to 
manufacture  and  give  a  stiffer  structure  under  traffic.  An  odd 
number  of  panels  is  preferable  to  an  even  number,  because  the 
maximum  moment  will  be  less  and  because  the  structure  may  be 
made  symmetrical  about  the  center  line  with  regard  to  field 
splices. 

The  panel  lengths  must  be  chosen  so  as  to  give  an  efficient 
lateral  system  without  increasing  the  width  of  the  bridge  be- 
yond that  required  for  clearance  of  the  roadway.  For  a  single 
track  bridge  this  width  is  usually  about  16  ft.,  depending,  of 
course,  on  the  width  of  the  truss  members. 

The  economic  depth1  (46)  cannot  be  determined  with  any 
degree  of  certainty,  but  is .  usually  taken  at  from  one-fifth  to 
one-sixth  of  the  length  of  span.  The  deeper  the  truss  is  made 
the  stiffer  it  will  be  and  the  less  the  vibratory  stresses  will  be. 
It  is  found  that  considerable  variation  in  the  depth  will  effect 
the  weight  and  cost  but  little.  The  depth  must  be  made  suffi- 
cient to  allow  efficient  overhead  bracing  without  interfering 

'See  "Stresses  in  Bridge  and  Hoof  Trusses,"  by  W.  H.  Burr,  Art. 
76,  page  353. 

139 


140  LOADS.  Art.  56. 

with  the  clearances  required  by  the  traffic,  unless  a  pony  truss 
is  used.1 

Pin  connected  pony  trusses  are  not  desirable  because  of  the 
lack  of  efficient  transverse  bracing. 

56o  Loads.2  Most  specifications  give  a  series  of  wheel 
loads  representing  the  weights  of  two  locomotives,  followed  by 
a  uniform  train  load  which  is  to  be  used  in  designing  the  struc- 
tures. In  bridges  over  100  ft.  long,  if  an  equivalent  uniform 
load  is  used  which  will  give  the  same  center  moment  in  the 
span,  the  errors  in  the  stresses  will  not  be  large.  It  will  be 
necessary  to  use  several  different  equivalent  loads  for  different 
parts  of  the  structure,  as,  for  instance,  one  for  the  stringers,  one 
for  the  floor  beams  and  hip  verticals,  and  one  for  the  trusses. 
The  laibor  involved  in  obtaining  these  equivalent  loadings  for 
the  floor  beams  and  stringers  is  about  as  great  as  it  is  to  calcu- 
late the  stresses  directly,  so  the  wheel  loads  are  generally  used 
for  these. 

An  equivalent  uniform  load  is  usually  used  for  the  trusses 
(except  the  hip  verticals).  The  stresses  in  some  of  the  members 
will  be  too  large  and  in  some  too  small.  The  variation  will 
usually  be  less  than  about  4%  from  the  stresses  obtained  by 
using  the  actual  wheel  loads  specified.3 

Even  if  the  exact  loading  specified  should  ever  come  upon 
the  bridge,  the  stresses  calculated  from  the  wheel  loads  would 
not  be  the  true  stresses,  because  the  track  distributes  the  wheel 
loads  differently  from  what  we  assume,  and  the  stringers  are 
partially  continuous  while  we  assume  them  to  be  simply  sup- 
ported at  each  floor  beam.  Besides,  the  impact  or  vibratory 
stresses  cannot  be  estimated  with  less  than  a  probable  error 
amounting  to  many  times  the  discrepancy  in  the  stresses  ob- 
tained by  the  two  methods. 

Numerous  other  methods  of  obtaining  "equivalent"  load- 
ings have  been  proposed,  and  it  is  probably  due  to  the  disagree- 


VSee  Heller's  "Stresses  in  Structures,"  Art.  113  and  151. 
'See  Heller's  "Stresses  in  Structures,"  Art.  119,  130  and  131. 
•  See  Trans.  Am.  Soc.  C.  E.,  Vol.  42,  pp.  189,  215  and  206. 

Also  Johnson's  "Modern  Framed  Structures,"  Chapter  VI. 

Also  DuBois'  "Stresses  in  Frames  Structures." 


Art.  57.  TENSION  MEMBERS.  141 

ment  on  this  point  that  engine  loads  are  still  specified  in  all  but 
a  few  specifications,  and  that  some  engineers  still  calculate  all 
stresses  from  wheel  loads. 

The  dead  load  must  be  estimated.  The  weight  of  the  floor 
(52)  including  rails,  ties  and  guards  for  the  ordinary  floor 
construction,  with  stringers  not  over  6  ft.  6  in.  center  to  center, 
will  not  exceed  about  400  Ibs.  per  linear  foot  of  track.  The 
weight  of  the  steel  work  may  be  estimated  approximately  by 
comparison  with  some  previously  made  estimates  of  similar 
structures,  or  may  be  taken  from  an  empirical  formula  (52). 
After  the  design  and  estimate  are  completed,  the  dead  load  must 
be  revised  to  agree  with  the  final  estimated  weight,  if  the  dis- 
crepancy is  sufficient  to  change  the  size  of  any  of  the  members. 
(51)  (52). 

57.  Tension  Members.  The  tension  members  of  pin  con- 
nected trusses,  except  the  hip  verticals,  and  in  some  cases  ths 
counters  and  end  panels  of  the  lower  chord,  are  usually  made  of 
eye  bars.  The  counters  and  end  panels  of  lower  chord  are  fre- 
quently required  to  be  made  rigid  members,  to  increase  the 
stiffness  of  the  bridge.  The  hip  verticals  should  always  be  rigid 
members,  because  this  gives  a  better  connection  for  the  floor 
beams  at  these  points,  and  because  it  greatly  reducs  the  vibra- 
tion. 

Eye  bars  are  forged,  and  the  heads  are  made  of  such  size 
that  in  testing,  the  bar  will  break  in  the  body  instead  of  through 
the  head.  Usually  the  net  section  through  the  pin  hole  is  made 
about  25%  in  excess  of  the  section  through  the  body  of  the  bar.1 

Eye  bars  should  not  be  thinner  than  about  %  inch,  and 
should  not  be  too  thick,  say  over  about  2*4  inches.  Thick  bars 
will  usually  not  show  as  high  an  ultimate  strength  as  thin  ones. 
The  usual  proportions  of  width  to  thickness  lie  between  3  to  1 
and  7  to  1. 

Built  tension  members,  of  course,  contain  more  material 
than  tension  members  of  the  same  strength  made  of  eye  bars. 
The  net  section  through  rivet  holes  (11)  and  through  the  pin 
holes  must  be  carefully  investigated.  The  most  common  form 


1  Sizes  of  eye  bars  as  manufactured  by  that  company  are  given  in 
Cambria,  page  333. 


142  COMPRESSION  MEMBERS.  Art.  58. 

is  an  I  cross  section  made  of  four  angles  latticed  together,  al- 
though two  channels  latticed  are  frequently  used.  Sometimes 
two  eye  bars  are  laced  together  with  bent  bars,  but  this  does  not 
give  a  member  much  stiffer  than  the  plain  eyebar  member. 

The  required  net  area  of  a  tension  member  is  obtained  by 
simply  dividing  the  stress  in  the  member  by  the  allowed  unit 
stress  in  tension  as  given  by  the  specifications. 

58.  Compression  Members.  The  intermediate  posts  are 
usually  made  of  two  channels,  either  built  or  rolled,  latticed 
together.  Built  channels  are  of  course  more  expensive  than 
rolled  channels,  on  account  of  the  extra  punching  and  riveting. 

If  the  toes  of  the  channels  are  turned  in,  the  backs  form 
plane  surfaces  to  which  connections  may  be  more  easily  made 
than  if  the  toes  are  turned  out.  The  distance  in  the  clear  be- 
tween the  channels  must  be  great  enough  to  allow  the  entrance 
of  the  riveting  tool  between  the  lacing  bars,  and  it  is  economical 
to  place  the  channels  far  enough  apart  to  make  the  ratio  of  the 
unsupported  length  to  the  radius  of  gyration  in  the  two  direc- 
tions equal.1  Local  conditions  frequently  limit  the  dimensions 
of  these  members. 

Experiments  show  that  a  'Column  will  fail  at  an  average 
unit  stress  over  the  entire  cross  section,  which  is  less  than  the 
ultimate  strength  of  the  material  in  compression,  and  that  the 
longer  the  column  the  less  will  be  this  average  unit  stress  at 
failure.  In  other  words,  a  column  does  not  fail  by  compression 
alone  but  by  a  combination  of  compression  and  bending.2 

This  is  taken  into  account  in  the  design  of  compression 
members  by  the  use  of  a  "column  formula,"  which  gives  us  -an 
average  unit  stress  which  it  is  safe  to  allow  on  the  cross  section, 
and  after  this  unit  is  determined  the  design  of  the  compression 
member  is  as  simple  as  that  of  a  tension  member,  but  the  deter- 
mination of  the  average  unit  stress  allowable,  involves  properties 
of  the  cross  section  of  the  member,  so  the  solution  must  be  by 
trial. 


*See  Cambria,  page  221. 

2  For  an  excellent  article  on  Columns  see  editorial  in  Engineering 
News,  January  3,  1907. 


Art.  68. 


COMPRESSION  MEMBERS. 


143 


A  column  formuk  consists  of  a  variable  reduction  factor 
applied  to  the  maximum  allowed  fiber  stress  in  compression. 

The  column  theory1  assumes  that  the  whole  member  acts 
as  one  piece,  and  the  function  of  the  stay  plates  and  lacing  is  to 
hold  the  component  parts  of  the  member  in  line  and  to  insure 
its  action  as  a  unit. 

A  column  under  stress  will  deform  into  a  curve  with  a  point 
of  contra-flexure  near  each  end,2  the  distance  from 
the  end  depending  upon  the  degree  of  fixity  of  the 
end.  At  these  points  of  contra-flexure  the  bending 
moment  is  zero,  and  consequently  the  stress  on  the 
column  cross  section  is  uniform.  Midway  between 
these  points  the  maximum  bending  moment  occurs, 
and  the  maximum  unit  stress  in  compression  occurs 
on  the  concave  side,  therefore  in  a  distance  equal 
to  one  half  the  length  between  the  points  of  contra- 
flexure,  the  unit  stress  in  the  concave  side  of  the 
column  must  change  from  the  average  to  the  maxi- 
\p  mum  allowed. 
Fig.  64. 

Suppose  a  column  to  be  made  up  of  two  leaves 
connected  by  lacing  or  otherwise. 

Let  51=maximum  allowed  unit  stress  on  the  material 
in  compression. 

p 

sc=average  unit  stress  over  the  cross  section=  — 

A 
.F=total  change  in  stress  in  one  leaf  of  the  column 

in  a  distance  I. 
/=change  in  the  total  stress  in  one  leaf  per  unit 

F 

of  length=  — 


least  distance  from  the  point  of  maximum 
bending  moment  to  a  point  of  contra-flexure. 
L=total  length  of  column. 
^I1=area  of  cross  section  of  one  leaf. 

F=Ai  (si—  s  \  (16) 


I 


'See  Seller's  "Stresses  in  Structures,"  Chapter  X. 

•  See  Heller's  "Stresses  in  Structures,"  Fig.  137,  page  178. 


144  COMPRESSION  MEMBERS.  Art.  68. 

For  a  pin  ended  column  L—21  and  for  a  square  or  fixed 
ended  column  L=4d.  Any  column  in  practice  will  lie  somewhere 
between  these  two  limits,  and  in  any  case  eccentricities  of  manu- 
facture and  loading  may  make  I  different  than  theory  would 
indicate. 

Also  this  theory  assumes  that  the  rate  of  change  of  stress 
in  the  leaf  is  uniform,  which  is  not  true,  therefore,  to  be  on  the 
safe  side  we  will  take  L=41  in  all  cases ;  then 

4A(ft— sc)  (18) 

L 

Equation  (18)  gives  the  longitudinal  increment  of  stress 
in  one  leaf  per  unit  of  length  of  column,  and  sufficient  connec- 
tion must  be  provided  between  the  leaves  to  transmit  this  stress 
(49).  The  values  of  sx  land  sc  are  taken  from  the  column  for- 
mula which  is  being  used  unless  there  is  bending  due  to  trans- 
verse loads.  (77) 

When  lacing1  is  used  the  bars  must  be  capable  of  taking 
their  stress  either  in  tension  or  compression. 

The  top  chords  and  end  posts  are  usually  made  of  two  built 
or  rolled  channels,  connected  by  a  cover  plate  on  top  and  by  stay 
plates  and  lacing  on  the  bottom.  The  cover  plate  being  solid 
aids  in  taking  compression,  and  its  area  is  always  considered  in 
the  effective  cross  section.  The  cover  plate  then  serves  both  as 
a  part  of  the  compression  area  and  to  tie  the  two  leaves  of  the 
column  together. 

A  compression  member  with  a  cover  plate  on  one  side  only 
is  not  symmetrical  about  its  center  of  gravity,  and  the  end 
connections  must  be  designed  to  transmit  the  stresses  to  the  cross 
section  properly.  (10) 

The  cover  plates  should  always  'be  made  as  thin  as  the  speci- 
fications will  allow  unless  they  have  some  special  duty  to  per- 
form, so  as  to  keep  the  eccentricity  of  the  section  small.  The 
unsupported  width  of  plates  in  compression  (distance  between 
rivet  heads)  is  usually  limited  by  the  specifications  to  30  or  40 
times  the  thickness  of  the  metal 

If  a  compression  member  is  subjected  to  transverse  loads, 


1  For  various  methods  of  calculating  lacing  see  Report  of  the  Royal 
Commission  on  the  failure  of  the  Quebec  Bridge,  Appendix  No.  16, 
Also  the  Report  of  C.  C.  Schneider. 


Art.  58.  COMPKESSION  MEMBERS.  146 

causing  bending1  in  addition  to  the  direct  load  (40),  the  maxi- 
mum fiber  stress  due  to  both  must  not  exceed  the  maximum 
allowed  unit  compressive  stress  (sj,  and  to  be  on  the  side  of 
safety  should  not  exceed  a  unit  stress  determined  by  a  suitable 
column  formula  (sc),  because  the  accidental  eccentricities  may 
increase  the  bending  due  to  the  transverse  loading. 

The  horizontal  and  inclined  compression  members  are  .in 
bending  due  to  their  own  weight  in  addition  to  being  in  com- 
pression. In  the  top  chords  and  end  posts  of  bridges  this  bend- 
ing moment  is  partially  neutralized  by  lowering  the  centers  of 
the  end  connections  an  amount  sufficient  to  produce  an  upward 
bending  moment  due  to  the  eccentricity  of  the  compressive  stress, 
equal  to  the  downward  bending  moment  due  to  weight. 

,  wLP  /-nx 

and    e=—  (19) 


Equation  (19)  is  generally  used  in  practice  to  determine 
the  eccentricity  of  the  pins  to  compensate  for  the  bending  due 
to  the  weight  of  the  member.  Using  this  value  of  e  would  render 
the  bending  moment  almost  zero  at  the  middle,  but  as  the  bending 
moment  (Pe)  due  to  the  eccentricity  is  ia  constant,  while  the 
moment  due  to  the  weight  is  a  maximum  at  the  middle  and  zero 
at  the  ends,  the  use  of  this  value  of  e  produces  a  negative  bend- 
ing moment  at  the  end  as  great  as  the  original  moment  due  to 
the  weight.2  It  is  better  to  use  a  smaller  value  of  e  as  given  by 
equation  (20), 

If  ^  llllil  (2o) 

as  this  will  give  a  less  resultant  maximum  bending  moment  in 
the  column. 

Another  case  in  which  compression  members  are  subjected 
to  both  axial  and  bending  stresses  is  the  end  posts  of  a  through 
bridge  with  overhead  bracing.  The  end  posts  must  carry  the 
wind  load  in  bending  from  the  portal  to  the  abutments.3  This 
bending  is  in  a  plane  perpendicular  to  that  of  the  bending  due 
to  weight.  The  lacing  and  riveting  of  the  cover  plates  of  the 


*See  Heller's  "Stresses  in  Structures,"  Art.  Ill,  page  190. 
2See  Article  by  Prof.  J.  E.  Boyd  in  Engineering  News  for  April  11, 
1907,  page  404. 

3  See  Heller's  "Stresses  in  Structures,"  Arts.  153  to  165  inclusive. 


146  LATERAL  SYSTEMS.  Art.  59. 

end  posts  must  be  sufficient  to  transfer  the  increments  of  stress 
as  determined  by  equation  (17). 

59.  Lateral  Systems.1      In  a  through  bridge  a  lateral  sys- 
tem is  always  provided  in  the  plane  of  the  lower  chord  and,  if 
the  head  room  permits,  in  the  plane  of  the  upper  chord  also.    In 
a  deck  truss  bridge,  lateral  systems  should  always  be  provided 
in  the  plane  of  both  the  top  and  bottom  chords. 

The  top  lateral  system  in  a  deck  bridge  and  the  bottom 
lateral  system  in  a  through  bridge  is  assumed  to  take  all  the 
wind  load  on  half  the  projection  of  the  trusses,  the  floor  system 
and  the  train  and  the  centrifugal  force  if  the  track  is  on  a 
curve,2  although  a  small  part  of  the  latter  would  be  transmitted 
to  the  top  lateral  system  by  the  stiffness  of  the  intermediate 
posts. 

The  lateral  system  is  a  horizontal  Pratt  truss  in  which  the 
floor  beams  act  as  the  posts  and  the  chords  of  the  main  trusses 
act  as  chords.  The  diagonal  members  are  put  in  in  both  direc- 
tions to  provide  for  a  reversal  of  wind. 

The  top  lateral  system  in  a  through  bridge  and  the  bottom 
lateral  system  in  a  deck  bridge  take  the  wind  load  on  half  the 
projection  of  the  trusses. 

The  end  reaction  of  the  top  lateral  system  in  a  through 
bridge  is  conveyed  to  the  abutment  by  means  of  portal  bracing 
between  the  end  posts  and  by  bending  in  these  end  posts.8  (58) 

Provision  must  be  made  in  all  main  truss  members  carrying 
wind  stresses  for  these,  in  addition  to  the  dead  and  live  load 
stresses. 

The  wind  blowing  upon  the  side  of  a  train  on  a  bridge  tends 
to  overturn  it,  and  thus  produces  a  greater  load  on  the  leeward 
truss  than  on  the  windward.  The  effect  on  the  top  chord  of  a 
through  bridge  is  very  small  because  the  leeward  top  chord 
would  be  in  tension  under  the  wind  load  alone.  The  -bottom 
chords  and  web  members  should,  however,  be  proportioned  for 
this  additional  stress.  (63) 

60.  Design  of  a   Pin-connected   Railway  Bridge.       To 
illustrate  the  methods  of  solving  the  various  problems  connected 


*See  Heller's  "Stresses  in,  Structures,"  Chapter  XIV. 

3  See  Heller's  "Stresses  in  Structures,"  Art  166. 

'See  Heller's  "Stresses  in  Structures,"  Arts.  153  to  1«65  inclusive. 


Art.  61. 


DEAD  LOAD. 


147 


with  the  design  of  truss  bridges,  the  design  for  a  through  Pratt 
truss  railway  bridge  will  now  be  worked  out. 
We  will  assume  the  following  data : 

Span  189  ft.  c.  to  c.  of  end  pins  =  7  Panels  at  27  ft. 

Single  track.    Alignment  tangent. 

Specifications  Cooper's  1906  for  Railway  Bridges. 

Loading  Cooper's  E  40. 

Material  medium  steel  except  rivets. 

61.  Dead  Load.       (56)     The  stringers  will  be  spaced  6  ft. 
6  in.  c.  to  c.,  and  the  size  of  the  tie  may  be  calculated  as  was 
done  in  Art.  52.    We  will  use  8"x  8"  ties  10  ft.  long  spaced  14 
in.  c.  to  c.,  guard  rails  6"x8".     The  weight  of  the  floor  comes 
out  somewhat  less  than  400  Ibs.  per  lin.  ft.,  but  the  specification 
§23  directs  that  not  less  than  400  Ibs.  per  linear  ft.  shall  be 
used.     (51) 

The  weight  of  the  steel  work  may  be  approximately  esti- 
mated from  equation  (15),  w=7L+600  from  which  t<*=1923 
Ibs.  per  lin.  ft.  of  bridge.  The  total  dead  load  then  will  be 
1923+400=2323  Ibs.  per  lin.  ft.  of  bridge,  one-third  of  which 
will  be  considered  as  acting  at  the  top  chord  and  two  thirds  at 
the  bottom  chord. 

62.  The  Depth    of  the  trusses  (55)  must  be  sufficient  to 

allow  the  required  head  room 
and  also  an  efficient  portal. 
The  depth  of  the  floor  system 
will  govern  this  to  some  ex- 
tent also. 

An  estimate  of  the  depths 
required  for  these  various 
parts  may  be  made  and  an  ap- 
proximate minimum  allowed 
depth  calculated  in  the  form 
of  a  table  similar  to  the  one 
outlined  in  Art.  28. 

The  stringer  may  be  de- 
signed before  this  table  is 
made  up,  as  the  depth  of  the 
truss  does  not  effect  it.  We 
will  use  the  stringer  as  de- 
signed in  Art.  51,  for  this 
bridge. 


Fig.  55. 


148 


STRESSES. 


Art.  63. 


Depth  of  tie  over  stringer  ............   0'-7%" 

Depth  of  stringer  ...................  4'-3%" 

Bot.  of  stringer  to  bot.  of  Fl.  Bm  ......  0'-6%" 


(Spec.  §12) 


Bot.  of  Fl.  Bm.  to  Pin  Cent, 


101/4 


Base  of  Bail  to  Pin  Cent 4'-7" 

Required  Clearance    21'-0" 

Portal  depth  say 4'-5" 


(Spec.  §4) 
(min.) 


Total  depth  c.  to  c.  of  pins 30'-0"         (min.) 

The  depth  should  be  about  %  to  %  the  span  (55),  so  we 
will  use  a  depth  of  32/-0//  c.  to  c.  of  pins. 

63.  Stresses.       For  all  of  the  truss  members  except  the 
hip  verticals,   an   equivalent  uniform  live  load  will  be  used, 


Flem 


Dead 
Loat/ 


i/n/form 


JLoac/s 


Wax* 


aB  +/23/00 


264500 


31300 


Be 


-  &Z/00 


-/30000 


±    22400 


-22400 


Cd 


-  4/O00 


-/Z/600 


±    J4SOO 


-     o 


-  74000 


i    3000 


-    9000 


£>'c 


-  3&500 


ez/o0 


3600 


Bb 


-  20900 


^  30/00 


±     8000 


Cc 


-4/800 


33000 


96300 


6900 


-  79400 


-/64700 


±    20200 


Ac 


-  79*00 


L-/  '70  '600 


i  20200 


S36000 


±  33700 


-A58&00 


-330/00 


±  /63200 


BC 


/3230O 


274*500 


+2T4&00 


f  33700 


33700 


C£> 


+330/00 


*  ,40400 


Z7200 


+  -40400 


1-  27200 


derived  from  the  maximum  live  load  moment  for  the  span.  (56) 
This  equivalent  uniform  load  for  a  189  ft.  span  is  4820  Ibs.  per 
lin.  ft.  of  track. 


Art.  63. 


STRESSES. 


Panel  load  of  Dead  Load= 


2323  X  27 


=31,360  Ibs. 


Panel  load  of  Live     Load=  482°  X  27=65,070  Ibs. 

2 

The  table  under  Fig.  56  gives  the  direct  stresses  in  all  of 
the  truss  members  due  to  dead  load,  live  load,  and  wind.  The 
live  load  stresses  calculated  from  the  wheel  loads  are  also  given 
in  a  parallel  column  for  comparison.  The  maximum  error  is 
seen  to  be  in  the  end  posts  and  amounts  to  about  3^%. 

The  wind  stresses  in  the  chords  from  the  lateral  systems  are 
gotten  by  assuming  that  the  trusses  are  16'-0"  c.  to  c.  This 

will    not    be     far 
from  right. 

According  to 
specifications,  §24, 
450  Ibs.  of  the 
wind  laad  shall  be 
treated  as  acting 
on  a  moving  train 
s?/0AAs.  at  a  height  of  six 
feet  above  the  base 
of  rail.  This  gives 
a  height  of  6.0+ 
4.58  =  10.58  feet 
•above  the  pin  cen- 
ters. The  hori- 
zontal force  acting 
at  this  height  (see 
Fig.  57)  will  be 
450X27  =12,100 

K"          " "~          ''  '     **  Ibs.  per  panel.  The 

Fig'  57<  additional  load  on 

the  leeward  truss  at  each  panel  due  to  this  overturning  moment 
will  be 


12100X10.58 
16 


=8,000  Ibs. 


The  additional  stress  in  each  member  then  will  be  the  direct 
live  load  stress  in  the  member,  (figured  for  the  equivalent  uni- 

soon 
form  load)  multiplied  by 


65070 


150  DESIGN  OF  TENSION  MEMBERS.  Art.  64. 

The  specifications  §39  directs  that  the  stresses  in  the  truss 
members  due  to  wind  may  be  neglected  unless  they  exceed  30% 
of  the  combined  dead  and  live  load  stresses.  Therefore  we  will 
have  to  consider  the  wind  stresses  only  in  the  bottom  chords. 
The  bending  in  the  end  posts  due  to  the  portal  stresses  will  be 
taken  up  in  Art.  66. 

64.  Design  of  Tension  Members.  The  required  net  area 
for  any  tension  member  is  obtained  by  adding  algebraically,  the 
areas  required  for  dead  load  -and  live  load  stresses.  (Spec.  §31 
and  35).  There  is  also  a  limiting  clause  for  counters.  (Spec. 
§50  and  51.) 

Since  in  these  specifications,  the  dead  load  unit  stress  is 
just  twice  the  live  load  unit,  the  same  area  will  be  obtained  if 
the  live  load  stress  plus  half  the  dead  load  stress  be  divided  by 
the  live  load  unit  stress. 

From  this  relation  we  may  derive  an  average  unit  stress 
which  may  foe  applied  to  the  total  dead  plus  live  load  stress  in 
any  member  as  follows: 

average  unit  stress, 
s^^the  dead  load  unit  stress. 
8L=^hQ  live  load  unit  stress. 
D=the  dead  load  stress  in  the  member. 
l>=the  live  load  stress  in  the  member. 
Then 

D+L  2(D+L)sL  1sL 

— — — —      — 


SD 


It  is  not  necessary  to  find  this  average  unit  stress  except 
for  those  members  in  which  the  wind  stress  must  be  taken  into 
account  according  to  specifications  §39. 

The  simplest  members,  those  made  up  of  eye  bars,  will  be 
proportioned  first.  We  will  assume  that  we  are  limited  in  the 
choice  of  eye  bars  to  those  manufactured  by  the  Cambria  Com- 
pany, as  indicated  in  their  hand  book,  pages  332  and  333. 


Art.  64.  DESIGN  OF  TENSION  MEMBERS.  151 


£$2100 

Be         Required  D.  L.  Area=!  —  —  =4.11  sq.  in. 

20000 


Required  L.  L.  Area=  —    -=18.24  sq.  in. 

10000        _ 

Total=22.35  sq.  in. 

This  may  be  made  up  of  4  bars  6"x|£  "  (iarea^=22.50  sq.  in.) 
or  2  bars  7"xl%"  (area=22.76  sq.  in.).  The  6  inch  bars  are 
slightly  more  economical  and  will  not  require  such  large  heads 
so  we  will  use  4  bars  6"x|£"  for  Be. 

41000 

Cd        Required  D.  L.  Area=  -  •  =  2.05  sq.  in. 

20000 

-D        •     j   T     T  121600        -,0  -i/? 

Required  L.  L.  Area=  --  =12.16  sq.  in. 

10000 

Total=14.21  sq.  in. 

This  wiU  require  2  bars  G^xl^"  (area=14.25  sq.  in.) 
Dd'      Required  D.  L.  Area=00 


Required  L.  L.  Area=    —  —     =7.3  sq.  in. 

This  will  require  2  bars  4"x-}£"  (area=7.50  sq.   in.)   or 

2  bars  3"xli4"  (area=7.50  sq.  in.).    The  3  inch  bars  cannot  be 
used  because,  probably  the  size  of  the  pin  at  d  will  exceed  5  in., 
which  is  the  largest  size  that  the  table  in  Cambria  gives  for  a 

3  inch  bar,  so  we  will  use  2  bars  4"x{-£" 

An  increase  in  live  load  of  25%  or  to  E50,  will  increase  the 
unit  stress  in  this  counter  exactly  25%  so  §51  of  the  specifica- 
tions is  satisfied. 

D'c'     Required  D.  L.  Area=  -^°  ^.05  sq.  in. 

20000 

36500 
Required  L.  L.  Area=  —  -—=3.65  sq.  in. 

Diff€rence=l  .  60  sq.  in. 

To  comply  with  specifications  §51  an  increase  in  live  load 
of  25%  must  not  increase  the  unit  stresses  more  than  25% 
therefore  : 


Required  D.  L.  Are^  =1  .  64  sq.  in. 


Required  L.  L.  Arefr=36500  +  25^°  =3  .  65  sq.  in. 
10000  +  25% 

Difference=2  .  01  sq.  in. 


152 


DESIGN  OF  TENSION  MEMBERS. 


Art.  64. 


This  will  require  1  bar  lT\in.  square  (area=2.07  sq.  in.). 
cd.     The  average  unit  stress  allowable,  as  determined  by 
equation  (21)  must  be  used  here  because  the  wind  stress  is  more 
than  30%  of  the  dead  and  live  load  stresses.     (Spec.  §39.) 

20000 
$w=        274~5~  — Hj940  Ibs.  per  sq.  in. 

1+   406.8 

11,940+30  %=15,520  Ibs.  per  sq.  in. 

Total  stress  in  cd=132.3+274.5+169.7=576.5. 


-o        •     j     A  576500      0_  -  A 

Required  Area=  • =37.14 

15520 


sq.   in. 


This  will  require  4  bars  6"xlTy  (area=37.50  sq.  in.)  or 
2  bars  7"xl  Ty  plus  2  bars  7"xl3/8"  (area^=37.64  sq.  in.) 

The  7  inch  bars  will  be  better  because  the  thickness  is  less, 
and  this  will  give  a  less  bending  moment  on  the  pin,  and  also 
probably  the  next  chord  dd'  will  necessarily  be  made  of  7  inch 
bars,  in  which  case  the  same  dies  may  be  used  for  making  all 
of  the  eye  bar  heads  in  the  bottom  chords,  which  would  reduce 
the  cost. 

dd'      Total  stress=158.8+329.5+203.6=691.9 
Allowed  unit  stress=15,520  Ibs.  per  sq.  in. 


Required  Area= 


15520 


=44.58  sq.  in. 


This  will  require  2  bars  7"xl%"  plus  2  bars  7"xl  •&"  (area 
=44.64  sq.  in.). 

According  to  the  specifications  §10  the  vertical  suspenders 
and  the  two  end  panels  of  lower  chord  must  be  miade  rigid 
members. 

abc      Total  stress=79  .  4+164.7+101.8=345.9 
Allowed  unit  stress=15,520  Ibs.  per  sq.  in. 


Required  Area= 


15520 


=22.29  sq.  in. 


Fig.  58. 


This  member  may  be  made  "up  of  4  angles 
and  2  plates  laced  together  horizontally  as 
shown  in  Fig.  58.  We  will  use  4  angles 
6"x3%"x%",  and  2  plates  14  inches  wide  by 
as  thick  as  may  be  necessary  to  make  up  the 
required  net  area.  To  comply  with  specifica- 
tions §64  at  least  two  rivet  holes  must  be 
deducted  from  each  angle.  (11) 


Art.  64.  DESIGN  OF  TENSION  MEMBERS.  153 

Net  area  4  angles  6"x3%"x%"  =  18.00  -  8xlx%  =  14.00 
sq.  in. 

Required  net  area  of  plates=22.29— 14.00=8.29  sq.  in. 
Equivalent  net  width,  of  plates=14— 2x1=12  inches. 

8  29 

Required  thickness  of  plates=— — =0.69  inches. 

12 

Use  2  plates  14"x%".    Total  actual  net  area 

2  Angles    6//x3y2"xi/2/'=14.00  sq.  in.  net 
2  Plates  14"x3/8"=  9.00  sq.  in.  net 


Total=23.00  sq.  in.  net 

It  would  be  more  economical  to  use  four  angles  without 
cover  plates,  but  it  is  not  well  to  use  metal  thicker  than  about 
%  in>ch  in  a  riveted  tension  member,  besides,  according  to 
specifications  §129,  material  over  %  inch  in  thickness  in  tension 
members  must  be  reamed,  which  would  increase  the  cost  con- 
siderably. 

Bb  will  be  made  of  two  roiled  channels,  and  will  be  made 
the  same  width  as  the  intermediate  posts  Cc  and  Dd  so  that  the 
floor  beams  may  all  be  made  alike. 

The  allowed  unit  stresses  are  less  for  verticals  carrying 
floor  beams  than  for  other  truss  members  (Spec.  §31). 

Required  D.  L.  Area= =  1 . 31  sq.  in. 

16000 

Required  L.  L.   Area=  &^£  =10 . 01  sq.  in. 

8000 

Total=11.32  sq.  in. 

There  will  be  pin  plates  on  the  webs  of  the  channels  for 
the  connection  at  B,  and  stay  plates  riveted  to  the  flanges  near 
them.  These  will  make  it  necessary  to  take  at  least  4  holes  out 
of  each  channel  as  shown  in  Fig.  59. 

The  member  cannot  be  made  of  less  than  10  inch  channels 
or  there  would  not  be  room  for  the  floor  beam 
connection.  The  lightest  weight  10  inch  channel 
cannot  be  used  because  specifications  §82  re- 
quires that  no  metal  less  than  %  inches  thick 
be  used,  and  the  web  of  a  10"  by  15  Ib.  channel 
is  only  0.24"  thick. 
Fig.  59. 


164:  DESIGN  OF  COMPKESSION  MEMBERS.          Art.  65. 

2  _  10"X20  Ib.  channels  is  about  the  smallest  section  that  can  be 
used. 

The  rivets  in  the  flanges  cannot  be  larger  than  %",  (see 
Cambria,  page  53),  while  it  is  desirable  to  have  the  rivets  in  the 
web  %"  for  the  floor  beam  connections. 

The  net  area  then  of  the  2  channels  10"x20  lb.=11.76— 
4x  jSg-  x%—  4x0.38x1=8.71  sq.  in.  As  this  is  less  than  the 
required  area  we  must  use  heavier  channels.  Try  2  channels 
12"x25  Ibs.  Net  area=14.70—  4xi/2x%—  4x0.39x1=11.39  sq.  in. 
These  will  answer. 

65.  Design  of  Compression  Members.  The  least  allowable 
section  for  a  post  is  2  channels  10"x20  Ibs.  (See  Spec.  §§35  and 
82.)  The  greatest  allowed  length  for  a  post  composed  of  these 
channels  is  100  times  the  radius  of  gyration  (Spec.  §35)= 
100X3.66=366  inches=30/—  6",  which  is  less  than  the  depth  of 
our  truss,  so  a  larger  section  must  be  used.  Try  2  channels 
12"x25  Ibs.  Allowed  length=100X4.43=443"=36'-ll". 

AUowed  unit  stress  for  D.  L.=17000—  90  — 
=17000-. 


4.  43 
Allowed  unit  stress  for  L.  L.=  4600  Ibs.  per  sq.  in. 


Dd      Required  D.  L.  Area=-=  1.14  sq.  in. 

Required  L.  L.  Area=  $jj^  =12  .  13  sq.  in. 

Total=13.27  sq.  in. 

Actual  area^=2X  7.35=14.70  sq.  in.  which  is  sufficient. 
Cc.    The  stresses  for  this  post  are  considerably  greater  tha* 
for  Dd,  so  we  will  try  2  channels  15"x33  Ibs. 

Allowed  D.  L.  unit  stress=10,850  Ibs.  per  sq.  in. 
Allowed  L.  L.  unit  stress=  5,420  Ibs.  per  sq.  in. 


Required  D.  L.  Area=.^  3.86  sq.  in. 


Required  L.  L.  Area=  --  =17  .  16  sq.  in. 


Total=21.02  sq.  in. 

Actual  area  2  channels  15"x33  lbs.=2X  9.90=19.80  sq.  in, 
Try  2  channels  15"x40  Ibs. 


Art.  66.          DESIGN  OF  COMPRESSION  MEMBERS.  166 

Allowed  D.  L.  unit  stress=10,650  Ibs.  per  sq.  in. 
Allowed  L.  L.  unit  stress=  5,320  Ibs.  per  sq.  in. 


Required  D.  L.  Area=  —  —  =  3.93  sq.  in. 

10650 

Required  L.  L.   Area= — - —  =17.48  sq.  in. 

Total=21.41  sq.  in. 

Actual  area  2  channels  15"x40  lbs.=2X  11.76=23.52  sq.  in., 
which  is  sufficient. 

In  the  above  calculations  for  the  posts  we  have  (assumed 
that  the  ratio  of  unsupported  length  to  radius  of  gyration  in 
the  direction  parallel  to  the  webs  of  the  channels  was  greater 
than  that  in  the  other  direction  (58).  In  order  to  make  the 
posts  safe  according  to  the  specifications,  the  distance  between 
channels  must  be  sufficient  so  that  the  allowed  unit  stress  is 
greater  than  the  actual. 

The  actual  unit  stress  on  Cc= =5730  Ibs.  per  sq.  in. 

From  equation  (21)  the  allowed  unit  stress 

=  [~  17000—90  —  1  I  931=10060-53.26  — 

rJV+m5/ 

Equating  these  two  units  we  get 

5730=10060-53.25  ?i*!?fr®m  which  ^=3.1  in. 
r 

This  is  assuming  that  the  post  is  supported  by  sway  bracing 
at  an  elevation  of  21  ft.  above  the  floor  beam.  (Spec.  §107). 

The  distance  apart  of  the  channels  necessary  to  make  the 
radius  of  gyration  equal  to  3.1  in.  will  now  be  calculated. 

r=  J  JL         1=1  o  +Ad?  in  which 

\  A 

f^^moment  of  inertia  of  channels  about  their  own  center 
of  gravity. 

d— distance  from  the  center  of  gravity  of  the  column  to  the 
center  of  gravity  of  the  channel. 

=3.1  from  which 


d2=8.81        d=2.97  inches 
The  minimum  distance  back  to  back  of  channels  (toes  turned 


166.  DESIGN  OF  COMPRESSION  MEMBERS.          Art.  85. 

in)  then  will  be  2X2.97+2X0.78=7.5  inches,  but  Spec.  §35 
says  that  the  least  width  of  post  permissible  is  10  inches,  so  we 
will  use  this  width. 

The  post  Dd  will  be  made  the  same  distance  back  to  back 
in  order  that  the  floor  beams  may  be  made  alike. 

The  width  of  the  top  chord  and  end  posts  must  be  made 
the  same  throughout,  and  the  depth  of  the  two  are  usually  made 
the  same,  although  this  is  not  absolutely  necessary. 

The  width  must  be  sufficient  to  allow  all  of  the  web  members 
to  connect  to  the  pins  inside  of  the  top  chord  section.  In  some 
cases  a  pair  of  eye  bars  are  allowed  to  connect  to  the  pin  outside 
the  chord  section,  but  this  is  unusual. 

There  are  more  members  connecting  at  B  than  at  any  other 
point,  so  the  required  width  there  will  be  determined. 

We  can  only  estimate  this  width  approximately  .at  present. 

Width  of  Bb  back  to  back  of  channels^  10" 

Pin  plates  on  Bb  say  2— 1/2"  =    V 

Bars  Be  2— 1|"  (2  inside  Bb)  =1%" 

Webs  of  end  posts  say  2—3,4"  =1%" 

Pin  plates  on  end  posts  say  2—%"  =    V 

Top  angles  on  end  posts  say  2—3"  =    6" 

Clearances  say  1%" 

Total=22i/2" 

In  order  to  make  sure  that  we  have  sufficient  clearance  we 
will  make  the  cover  plate  of  the  chord  24  inches  wide. 

The  depth  of  the  chord  section  must  be  made  sufficient  so 
that  there  is  room  between  the  pin  and  the  cover  plate  for  the 
connection  of  the  members.  The  pin  will  be  somewhat  above 
the  geometric  center  of  the  web  plates  because  the  center  of 
gravity  of  the  section  will  be  above  the  center  of  the  web. 

Assuming  this  eccentricity  of  the  pin  to  be  1%"  and  that 
the  radius  of  the  largest  eye  bar  head  is  not  over  7%",  we  have 
9"  as  the  half  depth  of  the  web  required  by  the  clearances. 

Figure  60  shows  about  the  dimensions  of  the  minimum 
chord  section  which  we  can  use  here. 


Art.  65. 


DESIGN  OF  COMPRESSION  MEMBERS. 


157 


The  specification  §80  requires  that  the  thickness  of  plates 
in  compression  shall  not  be  less  than 
3*0  of  the  unsupported  width,  except 
for  the  cover  plates  of  top  chords  and 
end  posts  which  are  limited  to  TV 
The  unsupported  width  of  the  plate 
is  the  distance  between  rivet  heads. 
For  the  cover  plate  it  will  be  (1) 
21i/4"-lTY'=19  Vf".  The  minimum 
Fig.  60.  allowed  thickness  of  cover  plate  then 


will  be 


will  be 


19.8 


30 


=%".  The  minimum  allowed  thickness  of  web  plate 
=0.45"  or  say  %"  also. 


For  the  chord  sections  CD  and  DD  we  will  try  the  following, 
which  is  about  the  least  chord  section  allowable  ias  we  have  seen: 


2  Web  plates 

1  Cover  plate 

2  Top  angles 
2  Bot.  angles 


18"X%'/S=48-(W  sq.  in. 

24"xy2"=12.00  sq.  in. 
3"X3"X%"=  4.22  sq.  in. 
4"X3"X%"=  4.98  sq.  in. 


Total=39.20  sq.  in. 

We  will  now  find  the  location  of  the  center  of  gravity  of  the 
cross  section  by  taking  moments  of  areas  about  the  upper  side 
of  the  cover  plate  (see  Fig.  60). 

Cover  plate  12 X  0.25=  3.00 
Top  angles  4.22X  1.39—  5.86 
Web  Plates  18.00X  9.62=173.25 
Bot.  Angles  4.98X17.97=  89.49 

Sum=271.60 

Distance  of  center  of  gravity  from  top   of  cover  plate 
=  271J80  =6        .nches 
39.20 

The  distance  of  the  center  of  gravity  above  the  center  of  the 
web  plate=9.63— 6.93=2.7  inches. 

The  least  radius  of  gyration  is  required  to  be  used  in  the 
determination  of  the  allowed  unit  stresses.  This  will  be  about  a 
horizontal  axis  through  the  center  of  gravity,  and  is  equal  to 


158  DESIGN  OF  COMPRESSION  MEMBERS.  Art.  66. 

The  moment  of  inertia  about  this  axis  must  now  be  found.1 
This  is  done  by  adding  to  the  moment  of  inertia  of  each  con- 
stituent part  the  product  of  its  area  by  the  distance  squared,  of 
its  center  of  gravity  from  the  center  of  gravity  of  the  section. 

Cover  plate  24X(^)3=      0.25 

12.00X(6.68)2=  535.47 

Top  angles     2X1.76—      3.52 

4.22X(5.54)2=  129.52 


Web  plates"-  >7*^    '  =486.00 

18.00X(2.70)2=  131.22 

Bot.  angles      2X1.92=      3.84 

4.98X(H.04)2=  606.97 

Total  Moment  of  Inertia=1896 . 79 

From  which  we  get  the  radius  of  gyration  about  the  hori- 
zontal axis  through  the  center  of  gravity 

IftQft  7Q 

-lot/vj .  i «/  rt   ore  *      \\ 

89.20 

The  allowed  dead  load  unit  stress  is  20000-90— =15,800 

r 

from  specifications  §35. 

Required  D.  L.  Area= =10.05  sq.  in. 

looUU 

329600 

Required  L.  L.  Area=  —     -  =41 . 71  sq.  in. 

7900 

Total=51.76  sq.  in. 

The  area  of  cross  section  must  therefore  be  increased.    We 
will  try  the  following : 

2  Web  plates  18"X3/4"=27.00  sq.  in. 

1  Cover  plate  24"X1/2"=12.00  sq.  in. 

2  Top   angles     3//X3//XA/'=  4.88  sq.  in. 
2  Bot.   angles     4"X3"X%"=  7.98  sq.  in. 

Total=51.86  sq.  in. 

Eccentricity=1.68  in.        7=2494        r=6.93  in. 
The  change  in  the  radius  of  gyration  is  seen  to  be  very  small, 


*See  Heller's  "Stresses  in  Structures,"  Art.  67,  page  92. 


Art.  66. 


DESIGN  OF  THE  END  POSTS. 


159 


and  the  corresponding  change  in  the  allowed  unit  will  be  very 
small,  so  this  section  will  (answer. 

BC.  The  section  for  this  chord  will  lie  somewhere  between 
the  two  tried  above,  and  therefore  we  may  use  the  same  allowed 
unit  stresses. 


Required  D.  L.  Area—  =  8.38  sq.  in. 

looOO 


Required  L.  L.  Area=  =34  .  75  sq.  in. 

7900         - 

TotaL=43.13  sq.  in. 
Use  the  following  section 

2  Web  plates  18"X  196/'=20.25  sq.  in. 

1  Cover  plate  24'/X1/2"=12.00  sq.  in. 

2  Top   angles       3"X3"X%"=  4.22  sq.  in. 
2  Bottom  angles  4"X3"Xi96"===  7.26  sq.  in. 

Total=43.73  sq.  in. 

Eccentricity=1.98  in.        7=2230        r=7.14  in. 
66.    Design  of  the  End  Posts.     Before  the  end  posts  can 
be  designed  the  stresses  in  them  due  to  the  portal  bracing  must 
be  determined. 


Fig.  61. 


160 


DESIGN  OF  THE  END  POSTS. 


Art.  66. 


From  Fig.  55  we  see  that  we  can  make  the  vertical  distance 
from  the  upper  clearance  line  to  the  upper  pin  center  6  ft.  5 
inches. 

Fig.  61  illustrates  the  method  of  determining  the  depth  of 
portal  which  we  may  use.  This  may  be  laid  out  to  scale  and  the 
depth  scaled.  For  the  purpose  of  calculating  the  stresses  the 
depth  does  not  have  to  be  determined  closer  than  the  nearest 
0.1  ft. 

In  the  following  calculations  of  the  stresses  in  the  end  posts 
and  portal  bracing  due  to  wind,  the  methods  and  notation  used 

in  Heller's  "Stresses  in  Structures," 
Arts.  153  to  165  inclusive,  will  be  fol- 
lowed. The  specifications  §106  directs 
that  the  portals  be  latticed  and  that 
they  be  connected  rigidly  to  the  end 
posts  and  top  chords. 

Fig.  62  gives  the  general  dimen- 
sions of  the  portal  bracing  and  end 
posts. 

First,  it  must  be  determined 
whether  the  end  posts  are  fixed  at  the 
ends  by  the  direct  stresses,  or  not. 

From  Fig.  60  we  may  determine 
approximately  that 

ki==k2=  about  17  inches=  dist, 
c  to  c  of  bearings  of  webs  on  pin. 

P=Panel  load  of  wind  load  on 
top  lateral  system=200X  27=5400 
pounds. 

lfc=Reaction  of  top  lateral  system  on  the  portal=2P  (there 
are  5  panels  in  the  top  lateral  system. )  =10,800  Ibs. 

To  test  for  the  degree  of  fixity  of  the  ends  of  the  posts  as- 
sume H=H'=y2(R+P)-  (Tnis  is  assuming  fixed  ends.)  Then 
JT=JT=8,100  Ibs. 

The  portal  being  rigidly  connected  to  the  end  posts  from 

B  to  F,  fixes  the  tops  of  the  posts,  then  the  point  of  contra- 

flexure  would  occur  midway  between  a  and  F  or  xl=x1f=l7.0  ft. 

#,=5^=8100X17=137,700    ft.    lbs.=l,652,400    in.    Ibs. 

With  moments  about  a  point  of  contra-flexure  we  get, 


Fig  62. 


Art.  66.  DESIGN  OF  THE  END  POSTS.  161 

-17.0) 
. 

=26,100  Ibs. 

The  maximum  stress  in  the  end  posts  occurs  in  the  leeward 
post  when  the  live  load  is  on  the  bridge  and  when  the  wind  is 
acting. 

Dead  Load  stress  =123,100  Ibs. 

Live  Load  stress  =255,400  Ibs. 

Overturning  tendency  due  to  wind  on  train=  31,300  Ibs. 
V  due  to  wind  on  top  lateral  system  —  26,100  Ibs. 

Total  maximum  direct  stress  =435,900  Ibs. 

The  concurrent  direct  stress  in  the  windward  post  will  be 
123,100+255,400-31,300-26,100=321,100  Ibs. 

The  moment  of  the  direct  stress  at  the  bottom  of  the  wind- 
ward post  tending  to  fix  the  end  is 

1/2&2Z)=321,100X1/2X17==2,729,400  in.  Ibs. 

As  this  is  greater  than  the  moment  M«  tending  to  rotate  the 
post  at  a,  the  posts  will  be  fixed  at  the  bottoms. 

The  maximum  bending  moment  in  the  post  occurs  either  at 
a'  or  at  F',  and  is  1,652,400  in.  Ibs. 

We  will  try  for  the  end  posts  the  same  section  as  was  used 
for  top  chord  sections  CD  and  DD. 

The  moment  of  inertia  must  be  calculated  for  a  vertical 
axis  through  the  center  of  gravity. 

Area  of  cross  seetion=51.86  sq.  in.      Eocentricity=1.68  in. 

I  (horizontal  axis)=  2494        r  (horizontal  axis)  =6.93 

/  (vertical  axis)  =3848 

The  average  allowed  unit  stress  for  dead  and  live  loads 
from  equation  (21) 

L 

17000—90 — 

r         10460      enAK  ,, 

5w= =  - ==6245  Ibs.  per  sq.  in. 

256400  1-675 

'+378500 

When  wind  stresses  are  added  to  the  dead  and  live  load 
stresses  this  unit  may  be  increased  30%,  (Spec.  §39),  making 
it  8120  Ibs.  per  sq.  in. 

For  this  cross  section  the  actual  maximum  fiber  stress 
would  be  (58) 


162  DFSIGN  OF  THE  END  POSTS.  Art.  66. 

P_     Mv      435900      1652400X12.876 

-          -         —  H 


=8405+5528=13933  Ibs.  per  sq.  in. 
Therefore  the  section  must  be  increased. 

As  the  moment  of  inertia  increases  when  the  area  is  in- 
creased, we  may  arrive  at  an  approximate  figure  for  the  area  by 
considering  the  equation  .above  as  follows: 

8405  :  5W=^13933  :  8120  from  which  5W=4900  Ibs. 

This  value  of  sw  .assumes  that  in  changing  the  section  we 
have  not  changed  the  radius  of  gyration,  land  of  course  can  be 
used  only  as  a  general  guide. 

Using  this  value  of  sw  we  find  that  the  approximate  required 

area  will  be435900=89  sq.  in.  about. 

It  will  be  found  by  trial  that  this  area  cannot  be  made  up 
without  materially  reducing  the  radius  of  gyration,  and  conse- 
quently the  allowed  unit  stress,  unless  the  width  or  depth  of  the 
section  be  increased. 

If  the  width  were  incresaed  it  would  necessitate  an  equal 
increase  in  width  of  the  top  chord  sections  and  add  materially 
to  their  weight  without  increasing  their  efficiency.  (See  Spec. 
§§80  and  100),  but  the  depth  of  the  end  posts  may  be  increased 
somewhat  without  changing  any  of  the  top  chord  sizes. 

After  several  trials  the  following  section  was  chosen: 

1  Cover  plate  24"X%"=15.00  sq.  in. 

2  Web  plates  21"X%"=36.75  sq.  in. 
2  Top  angles      3"X3"X%"=  6.72  sq.  in. 
2  Bot.  angles     4"X3"X%"=  7.98  sq.  in. 
2  Side  plates  15"X%"=18.75  sq.  in. 

Total=85.20  sq.  in. 

The  properties  of  this  section  are  as  follows  : 
Eccentricity=1.77  in.       Area=85.20  sq.  in. 
I  (horizontal  axis)  =4698       I  (vertical  axis)  =6424 
r  (horizontal  axis)  =7.43  in. 

Allowed  D.  L.  unit  stress=17000—  90-=10913  Ibs.  persq.  in. 

Allowed  unit  stress  for  D.  L.+L.  L.  from  Eq.  (21)=  6516 
Ibs.  per  sq.  in. 


Art.  67.  THE  PORTAL  BRACING.  163 

Allowed  unit  stress  for  D.  L.  +L.  L.+Wind=8468  Ibs.  per 
sq.  in. 

435900  ,  1662400X12.875 
Max.  extreme  fiber  stress=^-^+  --  ^j— 

=5116+3312=8428  Ibs.  per  sq.  in, 

67.  The  Portal  Bracing.  The  maximum  stresses  in  the 
portal  bracing  will  occur  when  there  is  no  live  load  on  the 
bridge. 

The  direct  stress  then  in  the  leeward  post,  (assuming  fixed 
ends  as  above,  is  as  follows  : 

Dead  Load  stress=123,100  Ibs. 
V=  26,100  Ibs. 

Total=149,200  Ibs. 

The  concurrent  direct  stress  in  the  windward  post=123,100 
—26,100=97,000  Ibs. 

The  moment  of  the  direct  stress  at  the  bottom  of  the  leeward 
post  tending  to  fix  that  end  is 

i/2fc2Z>=149,200X1/2X  17=1,268,200  in.  Ibs. 

The  moment  M2  required  to  fix  that  end  is  1,652,400  in.  Ibs., 
therefore  the  posts  are  only  partially  fixed  at  the  bottoms,  the 
tops  are  fixed  by  the  construction.  An  approximate  mean  value 
of  Xt  and  x\  may  be  gotten  from  the  equation 


Neglecting  V  in  the  value  of  D  we  get 

in.=10.75  ft. 


We  may  now  get  an  approximate  value  for  V. 

1st  Approx.F=—  V'=—  (E+P)  (a+d-xm) 

6 

=-i—  X16,200(43~10.75)=32,300  Ibs. 
16.15 

2nd  Approx,  D     =123,100-32,300=  90,800  Ibs. 
2nd  Approx.  D'    =123,100+32,300=155,400  Ibs. 
2nd  Approx.  M2  =8.5  X  90,800=   771,800  in.  Ibs. 
2nd  Approx.  M2'  =8.5X155,400=1,320,900  in.  Ibs. 


2nd  Approx.  #'    =K#+P+       (W—  16) 


164  THE  PORTAL  BRACING  Art.  67. 

=46(16,200+  2x3*xi2  X549,100)=9110  Ibs, 
2nd  Approx.  H    =E+P-#'=7090  Ibs. 


2nd  Approx.  ^     =      —          = 
if       7090 

2nd  Approx.  x\   =^j=  = =145  in.=12.08  ft. 

2nd  Approx.  F=-F'=  —  [(.K+P)  (a+d—a^)— IT^aj^— ^)] 

6 

= — —  [16,200(43-9.08)  -9,110X3]  =32,330  Ibs, 

16.15 

As  this  value  of  V  does  not  differ  materially  from  the  first 
approximation  the  values  of  the  other  quantities  are  also  deter- 
mined closely  enough. 

Taking  a  section  Im  through  the  portal  and  a  center  of 
moments  at  the  bottom  flange  Fig.  62. 

Stress  in  top  flange=E+%P+fl —  V  — 

d  d 

=10800+2700+7090-^^-32,330  JL 

The  maximum  compression  in  the  top  flange  then  will  occur 
Where  x=Q  and  the  maximum  tension  where  x=b. 

Max.  Comp.  in  top  flange=33,100  Ibs.  (  +  ) 
Max.  Tens,    in  top   flange=24,900  Ibs.   (  — ) 
Taking  the  same  section  and  a  center  of  moments  in  the 
top  flange 

Stress  in  bottom  flange  of  portal=#  —       —  —  V  — 

d  d 

The  maximum  tension  occurs  where  x=0  and  the  maximum 
compression  where  x=b. 

Max.  Tens,  in  Bot.  Flange=7090  -22^-  =26,700  Ibs.     (— J] 

9 

Max.  Comp.  in  Bot.  Flange=26700— 32330  -i^J£  ^=31,300 

Ibs.    (+) 

The  maximum  shear  at  any  section  is  T=32,330  Ibs. 

For  the  portal  flanges  the  least  allowable  radius  of  gyration 

as  i  X14X12=1.4  inches.     (Spec.  §35). 


Art.  68.  DESIGN  OF  FLOOR  BEAMS.  166 

This  radius  of  gyration  is  taken  perpendicular  to  the  plane 
of  the  portal. 

Try  2  Angles  S'^S'^y  ,  5  inch  legs  outstanding. 
Area=2X2.41=4.82  sq.  in.  gross.    r=2A7  in. 

The  allowed  unit  stress=13,000—  60^"-=8920  Ibs.  per  sq.  in. 
Reqd.  area=  5^=3.71  sq.  in. 


These   are   large   enough   for  the   maximum   compression 

stress. 

OAtrAA 

The  required  net  area  for  tension=—  —  -  =1.48  sq.  in. 

18000 

Actual  net  area=4.82—  2X  AXl=4.20  sq.  in.  (%"  Rivets.) 

For  the  lattice,  of  the  portals  we  will  use  angles  spaced  about 
as  shown  in  Fig.  62. 

Any  vertical  section  will  cut  four  lattice  angles,  and  we  will 
consider  the  shear  as  equially  divided  among  them. 

The  secant  of  the  angle  of  inclination  of  the  lattice  is  about 

OOQQA 

1.4,  so  the  stress  in  each  lattice  angle^l^X-^y^^H^OOlbs. 

tension  or  compression. 

The  smallest  angles  allowable  to  use  are  S'^i^"*^  ,  (See 
Spec.  §83),  which  will  be  ample  to  take  the  above  stress. 

68.  Design  of  Floor  Beams.  The  weight  of  the  beam  itself 
is  a  uniform  load,  the  weights  of  the  floor,  stringers  and  live 
load  form  two  concentrated  loads  on  the  floor  beam  6'-6"  apart. 
Since  the  beam's  own  weight  is  a  very  small  proportion  of  the 
total  load,  it  will  be  considered  as  concentrated  at  the  stringer 
connections  also. 

The  maximum  live  load  concentration  on  the  beam  may  be 
taken  from  the  specifications,  Table  I,  or  calculated  from  the 
wheel  loads. 

Live  load  at  each  stringer  connection=80,000  Ibs. 

Dead  load  from  floor  =200X27=  5,400  Ibs. 

Weight  of  stringers  =165X27=  4,455  Ibs. 

Weight  of  5%  ft.  of  floor  beam  say    =     945  Ibs. 

Total  Dead  Load=10,800  Ibs. 
at  each  stringer. 


166  DESIGN  OF  FLOOR  BEAMS.  Art.  68. 

The  distance  center  to  center  of  trusses  is  16  ft.  1%  in. 
This  is  considered  as  the  distance  between  supports  of  the  floor 
beams.     The  distance  between  the  center  of  the  truss  and  the 
nearest  stringer  connection  is  4'-9%"- 
The  moments  on  the  floor  beam  are  : 
Dead  load  moment=10,  800X4.  82=  52,060  ft.  Ibs. 
Live  load  moment=80,OOOX  4.  82=385,  600  ft.  Ibs. 
Economic  depth  from  equation  (10)    (no  flange  plates)  is 

' 


The  depth  assumed  in  the  calculations  for  the  depth  of  truss 
was  about  13  inches  more  than  the  depth  of  the  stringer,  or  64*4 
inches.  (See  Fig.  55). 

It  is  desirable  to  have  the  stringer  connection  come  between 
the  flange  angles  of  the  floor  beam  rather  than  to  have  it  lap 
over  the  vertical  legs  of  these  angles,  in  order  to  dispense  with 
filler  plates  under  the  connectian  angles.  For  these  reasons  then 
we  will  use  a  web  plate  64  inches  deep. 

The  maximum  shear=10,800+80,000=90,800  Ibs. 

Using  a  %"  web  plate  the  unit  shear=-^p=3780  Ibs,  per 

sq.  in.,  which  is  safe. 

Assuming  that  the  flange  angles  will  be  6"x6",  the  effective 
depth  will  be  about  61  inches. 

Approx.  D.  L.  flange  stress=5?^<l?=ioj240  Ibs. 

Approx.  L.  L.   flange  stress=885600X12  =75,860  Ibs. 

61 

10240 

Approx.  D.  L.  required  area=  -  =0.52  sq.  in. 


Approx.  L.  L.  required  area=  -  =7.59  sq.  in. 

10000        - 

Total=8.11  sq.  in. 

2Ls  6"x6"x  #'==10.12-4X&X1=8.37  sq.  in.  net.  (% 
inch  rivets,  no  holes  out  of  horizontol  legs,  two  holes  out  of  ver- 
tical legs,  to  comply  with  Spec.  §64.) 

The  'actual  effective  depth=64.25—  2X1.66=60.93  in. 

This  will  not  change  the  flange  stresses  given  above  appre- 
ciably, so  the  flange  as  designed  will  answer. 


Art.  68.  DESIGN  OF  FLOOR  BEAMS.  167 

There  must  be  sufficient  rivets  through  the  flange  angles 
and  web  to  develop  the  entire  flange  stress  between  the  end  of 
the  beam  and  the  stringer  connection.  This  will  require  more 
rivets  than  would  be  given  by  the  horizontal  increment  (49) 
because  the  flange  'angles  cannot  run  to  the  theoretical  end  of 
the  beam  which  is  at  the  center  of  the  truss. 

End  Floor  Beams  are  required  by  §10  of  the  specifications, 
and  it  is  always  good  practice  to  use  them  rather  than  to  allow 
the  end  stringers  to  rest  directly  on  the  abutments. 

The  end  floor  beam  must  carry  the  half  panel  load  from  the 
end  panel  of  the  bridge,  and  also  the  load  from  the  short  space 
between  the  end  floor  beam  and  the  back  wall,  which  is  usually 
bridged  by  a  cantilever  bracket  riveted  to  the  beam  opposite 
each  stringer.  This  space  will  be  about  two  feet  in  our  case. 

The  dead  load  at  each  stringer  connection  will  be 
Floor    (13.5+2.0)200=3100  Ibs. 
Stringer        15.5X165=2560  Ibs. 
Floor  Beam  say          =  840  Ibs. 

Total  D.  L.=6500  Ibs. 

The  live  load  reaction  at  the  stringer  connection  must  be 

determined  from  the  actual 
wheel  loads.  The  maximum 
reaction  on  the  end  floor 
beam  will  occur  with  the 
wheels  placed  as  shown  in 

Fig.  63. 

The  reaction  at  a=  178500°  =66,100  Ibs. 

27 

Dead  load  moment=  6,500X4.82=  31,300  ft.  Ibs. 

Live  load  moment=66,100X  4.82=31 8,600  ft.  Ibs. 

In  order  to  simplify  the  connection  of  the  end  floor  beam  to 
the  truss,  it  should  be  made  as  shallow  as  is  consistent.  We  will 
therefore  miake  the  depth  only  sufficient  to  -allow  the  stringer  to 
enter  between  the  horizontal  legs  of  the  flange  angles.  This  will 
require  a  depth  of  about  52%  or  53  inches. 

We  will  use  a  web  plate  53"x%". 

72fiOO 

Unit  shearing  stress= =3660  Ibs.  per  sq.  in.,  which  if 

19.07 

safe. 


168  DESIGN  OF  FLOOR  BEAMS.  Art.  68. 

The  effective  depth  will  be  about  51  inches. 

Approx.  D.  L.  flange  stress=81800xl2=  7,360  Ibs. 

51 

Approx.  L.  L.  flange  stress=318600X12  =75,000  Ibs. 

51 

7360 
Approx.  required  D.  L.  area='  -  =0.37  sq.  in. 


7^000 

Approx.  required  L.  L.  area=—  —  =7.50  sq.  in. 

10000        .  - 

Total=7.87  sq.  in. 

If  the  required  rivet  pitch  (49)  is  not  too  small  for  a  single 
line  of  rivets  in  the  flange,  we  may  use  unequal  legged  angles 
for  the  flange  with  the  long  legs  horizontal,  which  will  be  more 
economical. 

Try   2Ls    6"x3%"x%".     Net    area=9.00—  2X%X  1=8.00 
sq.  in.     (%  inch  rivets  and  no  holes  out  of  horizontal  legs.) 
Actual  effective  depth=53.25—  2X0.83=51.59. 

Actual  D.  L.  flange  stress=3130°X12=  7,300  Ibs. 

51.59 

Actual  L.  L.  flange  stress=  31860°X12   =74ji0o  Ibs. 


Actual  required  D.  L.  iarea= =0.37  sq.  in. 

20000 

Actual  required  L.  L.  area= =7.41  sq.  in, 

Total=7.78  sq.  in. 

This  will  not  allow  a  reduction  below  the  section  assumed 
above. 

The  number  of  rivets  required  to  connect  the  flange  angles 
to  the  web,  between  the  stringer  connection  and  the  end  of  the 
beam  will  be  the  total  flange  stress  81,400  Ibs.  divided  by  the 
value  of  a  %"  rivet  in  bearing  on  the  %"  web.  (See  Spec.  §40) . 

Number  of  rivets=?i^L  =21. 
3938 

The  distance  from  the  stringer  connection  to  the  end  of  the 
beam  will  be  about  3' -9". 

45 
Required  rivet  pitch=_  =2.12  inches,  which  is  less  than 

21 
should  be  allowed  in  a  single  line  (7).     (Spec.  §54).    Therefore 


Art.  69. 


TOP  LATERAL.  BRACING. 


169 


6"x6"  angles  must  be  used  for  the  flange  angles. 

Try  2Ls6"x6"x^0   Net  area=10.12 -4 XTVX  1=8.37 
sq.  in.    Actual  effective  depth=53.25— 2X1.66=49.93  in. 

Actual  D.  L.  flange  stres6=8380°X12=  7,500  Ibs. 
Actual  L.  L.  flange  stress=  318600X12  ==76,600  Ibs. 
Actual  required  D.  L.  area= 

Actual  required  L.  L.  area= 

i 

Total=8.04  sq.  in. 
Use  for  flanges  2Ls  6"x6"x A"« 

69.  Top  Lateral  Bracing.  (59)  The  top  lateral  system 
is  a  horizontal  Pratt  truss  of  five  panels,  with  the  portals  at  the 
ends  acting  as  .abutments. 

Panel  load  of  wind  load  for  top  lateral  system=200X27= 

5400  Ibs.    Sec*=5^£-==1.95. 
16.16 

The  stresses  are  as  follows : 

Diagonal  BC  =2X5400X1.95=21,100  Ibs. 
Diagonal  CD  =1X5400X1.95=10,600  Ibs. 
Diagonal  DD=Q 
Strut  CC=1%X5400=8,100  Ibs. 
Strut  DD=  i/2X5400=2,700  Ibs. 


£>' 


B' 


Fig.  64. 


21100 


Required  area  for  diagonal  BC= =1.18  sq.  in. 

18000 

To  comply  with  specifications  §11  the  lateral  bracing  must 
be  made  of  shapes  capable  of  resisting  compression.  It  is  not 
good  practice  to  use  angles  smaller  than  about  3%"x3"x  ty '  for 
these  laterals.  The  net  area  of  one  .angle  3%'/x3"x15G"=1.94— 
2  X  i66X  1=1.32  sq.  in.,  so  that  these  angles  will  answer  for  all 
the  diagonals. 


170 


BOTTOM  LATERAL  BRACING. 


Art.  70. 


The  size  of  the  intermediate  struts  will  be  determined  by 
§§35,  83  and  107  of  the  specifications.  The  unsupported  length 
will  be  about  170  in.  From  Spec.  §35  the  least  allowable  radius 


inches.      This    will    require   at    least 


of    gyration=— =1.42 

2Ls  3'/x2%"x156",  which  are  also  required  to  comply  with  §83 
of  the  specifications. 

Allowed  unit  stress=13,000— 60 — =6,000  Ibs.  per  sq.  in. 

T>       •     j  8100       .,  oc 

Required  >area= =1.35  sq.  in. 

6000 

Actual  area=2X  1.63=3.26  sq.  in. 

These  top  strut  angles  are  run  over  the  top  chords  and 
riveted  to  the  cover  plates,  and  two  other  angles  back  to  back 
are  riveted  between  the  intermediate  posts  as  low  down  as  the 
specified  head  room  will  allow  (See  Spec.  §107).  These  two 
struts  are  connected  by  diagonal  lattice  Avork  of  angles  similar 
to  the  portal  (See  Fig.  62). 

70.  Bottom  Lateral  Bracing.  The  bottom  lateral  system 
(Fig.  64)  must  resist  a  static  load  of  150  Ibs.  per  lin.  ft.  and  a 
moving  load  of  450  Ibs.  per  lin.  ft.  (Spec.  §24.) 

Panel  load  D.  L.  wind=150X27=  4,050  Ibs. 
Panel  load  L.  L.  wind=450X27t=12,150  Ibs. 
sec#=1.95  (same  -as  for  top  lateral  system). 
The  total  stresses  in  the  diagonals  -are  as  follows : 


Fig.  65. 


Diag.  a&=4050X3Xl.95+12,150X  3X1.95=94,700  Ibs. 

Diag.  6c=4050X2Xl.95+12,150XV-Xl.95=66,500  Ibs. 

Diag.  ccfc=4050XlXl.95+12,150X-V-Xl.95=41,700  Ibs. 

Diag.  «=405QXOX1.95+12,150X  f  Xl.95=20,300  Ibs. 

94700 
Required  area  a&= -=5.26  sq.  in. 

Required  area 


Art.  71.  SHOES  AND  ROLLERS.  171 

Required   area  cd=  -  =2.32  sq.  in. 

-D       •     j  jjr     20300 

Required  area  dd=  -  =1.13  sq.  in. 
18000 

To  comply  with  §33  of  the  specifications  both  legs  of  an 
angle  in  tension  must  be  connected  if  the  area  of  both  legs  is 
regarded  as  effective  section,  and  therefore  according  to  speci- 
fications §64  at  least  two  holes  must  be  deducted  from  the  gross 
section  of  each  angle. 

Use  for  diagonal  ab  2Ls  6"x3i£"x%".  Net  <area=6.86— 
4X%X1=5.36  sq.  in, 

Use  for  diagonal  be  2Ls  5"x3y2"x1Y'.  Net  area^=5.12— 
4X  AX  1=3.87  sq.  in. 

Use  for  diagonal  cd  IL  5"x4"x3/8".  Net  area=3.24—  2X% 
X  1=2.49  sq.  in. 

Use  for  diagonal  dd'  IL  S^xS'^Y'.  Net  area=1.94— 
2X156Xl=1.32sq.  in. 

The  bottom  flanges  of  the  floor  beams  act  as  the  bottom 
lateral  struts,  and  the  compression  from  the  lateral  forces  tends 
to  relieve  the  tension  in  them  from  vertical  loads. 

71.  Shoes  and  Rollers.  The  end  reaction  will  be  31/2  panel 
loads  of  Z>.L.+L.L.=3y2X96,430=337,500  Ibs. 

According  to  specifications  §113  this  will  require 


=1350  sq.  in.  bearing  on  the  masonry. 

The  masonry  plate  may  be  made  say  3'-6"  long  by  33  inches 
wide,  giving  a  bearing  area  of  1386  sq.  in.  According  to  speci- 
fications §114  the  rollers  cannot  be  made  less  than  5%  inches  in 
diameter. 

The  maximum  allowed  pressure  on  the  rollers  will  be 
300X53/4=1725  Ibs.  per  lin.  in. 

noire/-)  A 

Required  length  of  rollers=  -  =196  inches. 

This  might  be  made  up  of  6  rollers  33  inches  long,  or  7  rol- 
lers 28  inches  long.  The  details  can  not  be  worked  out  without 
detailing  the  end  posts,  end  floor  beams  -and  shoes. 

72.  Estimate  and  Stress  Sheet.  The  estimate  of  weight 
will  now  be  given.  The  details  can  only  be  estimated  approxi- 
mately until  the  detail  drawings  are  made.  Ordinarily  the 


172  ESTIMATE  AND  STRESS  SHEET.  Art.  72. 

details  are  put  in  the  estimate  as  a  percentage  of  the  main  truss 
members,  and  an  estimator  of  experience  in  detailing  and  es- 
timating can  choose  his  percentages  so  that  the  total  error  in 
weight  will  be  very  small. 

The  stress  sheet  may  now  be  drawn  up.     (See  Fig.  66.) 
This  is  usually  as  much  ias  is  done  until  after  the  contract 
is   awarded.      The  bridge   company  who   fabricates  the  work 
makes  the  detail  shop  drawings,  which  are  then  approved  by 
the  railroad  company's  engineer. 


THE  OHIO   STATE   BRIDGE  COMPANY 


Sheet  No.  _  Z  - 
Estimate  for • 


Made  by. 


Span  Extrem 
Roadw 

Sidewalk 

Capacity  Trusse 
Capacity  FIoo 
Specifications^^?/?/?. 


Span  C.  to 

/Panels  at->?Z-£l 

Depth  C.  to  C. 
Length  of  Diag. 

ff-t'fl 


Estimated  |    f  Steel  ---- 
DL  per  ft.  )    (  Floor  &  Track 


Panel  Lxwd  per  Truss 


Tota 

Steel  per  ft. 

Total  Lumber 


42.* 


44.6  42.0 


a& 


±574 


2L3-42* 


i/.-sr  42.5 


8 


im 


cv 


-73.0 


7.3 


O'c 


'•** 


49.4 


£± 


-&>+ 


23-P 


a*- 


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CHAPTER  VII. 
DETAILS  OF  PIN  CONNECTED  BRIDGES. 

The  design  of  the  bridge  and  stress  sheet  are  usually  worked 
out  'by  the  purchaser's  engineer  and  submitted  to  the  prospective 
bidders  for  prices,  but  sometimes  the  bidders  are  asked  to  submit 
designs  with  their  bids.  (16) 

After  the  contract  is  awarded  the  detail  shop  drawings  are 
made  by  the  contractor  and  approved  by  the  purchaser's  engi- 
neer. (See  Chapter  III.)  These  detail  drawings  show  the  sizes 
and  positions  of  all  connections  and  details  of  members,  together 
with  the  number  and  location  of  all  rivets. 

The  details  must  be  so  proportioned  that  the  stresses  will 
be  safely  and  economically  transmitted  from  member  to  member 
and  finally  to  the  abutments. 

73.  Pins.  A  pin  is  a  beam  which  transmits  the  stresses  at 
a  joint.  It  is  acted  upon  by  forces  in  different  planes,  which 
produce  bending  moments  and  shears  in  it. 

It  is  usually  convenient  to  resolve  these  forces  into  their 
vertical  and  horizontal  components  and  get  the  bending  moments 
in  these  two  planes  separately.  The  maximum  bending  moment 
at  any  point  then  is  the  resultant  of  the  horizontal  and  vertical 
moments  at  that  point.  Likewise  the  maximum  shear  at  any 
point  is  the  resultant  of  the  horizontal  and  vertical  shears  at  the 
point. 

Since,  in  most  cases,  the  maximum  stresses  in  all  of  the 
members  connecting  to  a  pin  do  not  occur  under  the  same 
loading,  the  condition  for  a  maximum  moment  in  the  pin  is 
uncertain,  and  the  moment  must  be  calculated  for  the  several 
conditions  which  give  maximum  stresses  in  the  various  members. 

In  proportioning  the  pin  for  shear  it  must  be  remembered 
that  the  maximum  intensity  of  shear  on  any  cross  section  of  a 
solid  cylinder  is  equal  to  four  thirds  the  average  intensity.1 

The  bearing  areas  of  the  members  on  the  pin  must  be  suffi- 
cient so  that  the  material  will  not  crush.  (10)  On  this  account 
it  is  well  to  have  large  pins,  because  the  larger  the  pin  the  less 
thickness  of  pin  plates  required,  and  also  there  will  be  less  danger 

*See  Heller's  "Stresses  in  Structures,"  Art.  71.     Also  Rankine's 
Applied  Mechanics,  Art.  309. 

177 


178  CALCULATION  OF  PINS.  Art.  74, 

of  unequal  distribution  of  stress  to  the  different  parts  of  a  mem- 
ber. For  example,  if  there  are  four  bars  in  a  panel  of  the  lower 
chord,  they  should  be  stressed  in  proportion  to  their  areas,  but 
this  will  not  occur  if  the  pin  should  bend  so  as  to  relieve  some 
of  the  bars  of  stress. 

On  the  other  hand,  the  larger  the  pins  the  larger  will  be 
the  diameters  of  the  eyebar  heads,  and  it  is  often  difficult  to  find 
room  for  them,  especially  at  the  hip  joint. 

The  arrangement  of  the  parts  of  the  members  on  the  pin  is 
called  the  packing,  and  this  should  be  such  as  to  produce  as  small 
a  moment  as  possible  on  the  pin  while  at  the  same  time  insuring 
that  the  eye  bars  do  not  pull  out  of  line  in  passing  from  joint  to 
joint,  more  than  about  one-eighth  of  an  inch  per  foot,  and  that 
the  riveted  members  are  of  constant  width  throughout  their 
length. 

The  sizes  of  pins  must  be  found  by  trial,  since  the  moments 
depend  upon  the  thicknesses  of  the  bearings,  and  to  get  these  we 
must  first  assume  a  diameter  for  the  pin. 

74.  Calculation  of  Pins.  A  few  of  the  joints  of  the  truss 
designed  in  Chapter  VI  will  now  be  detailed  to  illustrate  the 
methods. 

The  Hip  Joint.  (B).  According  to  §90  of  the  specifica- 
tions the  least  size  of  pin  which  may  be  used  here  is  0.8X6=4.8 
inches,  or  say  4%  inches. 

The  allowed  bearing  pressure  on  one  linear  inch  of  this  pin 
is  4%  X  12,500=60,940  Ibs.  for  live  loads  and  121,880  Ibs.  for 
dead  loads.  (See  Spec.  §41.) 

Required  bearing  on  end  post  aB 
^  128100 
121880 
TT       255400  -,ft   . 

LL= =4.19  in. 


60940 


Total=5.20  in. 

Required  bearing  on  top  chord  BC 
132300 
121880 

274500      ,   CA  . 

=4 . 50  in. 
60940       

Total=5.59  in. 


Art.  74  CALCULATION  OF  PINS. 

Required  bearing  on  hip  vertical  Bb 


179 


,    00   . 
=1.32  in. 


121880 

80100 
"  60940 

Total=1.49  in. 

The  bearing  pressures  on  the  eyebars  of  member  Be  ia 
taken  care  of  by  complying  with  §90  of  the  specifications. 

With  these  bearing  thicknesses  the  spacing  of  the  forces 
acting  on  the  pin  may  be  determined  approximately,  as  shown 
in  Fig.  67.  Sufficient  clearance  must  be  allowed  between  the 
different  parts  to  allow  them  to  be  easily  assembled. 

Fig.  67  shows  a  horizontal  projection  of  the  joint.    In  order 

to  render  the  bending  moment 
as  small  .as  possible  (Spec.  §90) 
the  eye  bars  should  be  packed 
as  near  their  resistences  as  pos- 
sible. 

The  bending  moments  and 
shears  will  have  to  be  calculated 
Fig.  67.  for   two    positions    of   the    live 

PACKING  AT  B.  load,  one  which  gives  maximum 

stresses  in  the  top  chord  end  post  and  hip  vertical,  and  one  which 
gives  a  maximum  stress  in  the  diagonal  Be. 

The  specifications  §41  permits  the  calculation  of  the  moments 
on  the  assumption  that  the  pressures  are  uniformly  distributed 
over  the  middle  half  of  the  bearing  areas.  The  moments  will  be 
only  slightly  increased  if  we  consider  the  forces  as  concentrated 
at  the  centers  of  the  bearing  areas,  and  this  will  greatly  simplify 
the  calculations.  This  assumption  is  usually  made. 

The  calculation  of  the  moments  is  best  made  in  tabular  form, 
remembering  that  the  moment  at  any  force  is  equal  to  the 
moment  at  the  next  preceding  force  plus  the  product  of  the  shear 
by  the  distance  between  the  forces. 

In  making  up  the  table  always  begin  at  the  outside  where 
the  shear  is  zero  and  work  toward  the  center  where  the  shear  is 
again  zero. 


180 


CALCULATION  OF  PINS. 


Art.  74. 


MAXIMUM  STRESSES  IN  aB  AND  BC 
MOMENTS  OF  HORIZONTAL  COMPONENTS. 


Mem. 

Horizontal 
Component 

Shear 

Lever  Arm 
in  inches 

MOMENTS 

Increment 

Total 

Be 

—  40700 

-  40700 

2 

-  81400 

BO 

+203400 

-  81400 

+162700 

f 

+122000 

aB 

—122000 

+  40600 

+  40700 

2 

+  81400 

Be 

-  40700 

+122000 

000 

2 

000 

Bb 

000 

+122000 

MOMENTS  OF  VERTICAL  COMPONENTS. 


Mem. 

Vertical 
Component 

Shear 

Lever  Arm 
in  inches 

MOMENTS 

Increment 

Total 

Be 

-  48200 

-48200 

2 

96400 

BO 

000 

-  96400 

—48200 

i 

3R1  ^fl 

aB 

+144600 

iqocKfl 

+96400 

2 

+192800 

Be 

—  48200 

+  60250 

+48200 

2 

+  96400 

Bb 

-  48200 

+156650 

The  maximum  for  this  loading  occurs  at  Bb  and  is 
1/(122000)2  +  (156660)2=198,730  in.  Ibs. 


MAXIMUM  STRESS  IN  Be. 
MQMENTS    OF    HORIZONTAL    COMPONENTS. 


Mem. 

Horizontal 
Component 

Shear 

Lever  Arm 
in  inches 

MOMENTS 

Increment 

Total 

Be 

-  42800 

-  42800 

2 

-  85600 

BO 

+184100 

-  8&fion 

+141320 

f 

+106000 

aB 

QQROO 

+  20400 

+  42800 

2 

+  85600 

Be 

.£00  AA 

+106000 

000 

2 

000 

Bb 

000 

+101000 

Art.  74. 


CALCULATION  OF  PESTS. 


181 


MOMENTS  OF  VERTICAL   COMPONENTS. 


Mem. 

Vertical 
Components 

Shear 

Lever  Arm 
in  inches 

MOMENTS 

Increment 

Total 

Be 

—  50500 

—50500 

2 

1  01  000 

101000 

BC 

—      000 

—60500 

t 

37KOO 

138800 

aB 

+116500 

+66000 

2 

+132000 

6800 

Be 

50500 

+15500 

2 

+  31000 

+  24200 

Bb 

—  15500 

The  maximum  resultant  moment  for  this  loading  occurs  at 
aB  and  is  |/(20400)2  +  (138800)2  =140,300  in.  Ibs. 

Then  the  maximum  bending  moment  on  the  pin  occurs 
under  full  loading  and  is  198,700  in.  Ibs. 

With  an  allowed  fiber  stress  of  18,000  Ibs.  per  sq.  in.  this 
will  require  a  4%  inch  pin,  (see  Cambria,  page  312),  or  exactly 
the  size  that  was  'assumed. 

The  maximum  shear  occurs  for  full  load  between  members 
BC  and  aB,  and  is  i/(l62700)2-K48200)2  =170,000  Ibs. 

4X1  70000 

This  gives  a  maximum  unit  shear  of  =12150  Ibs. 

3X18.  60 

per  sq.  in. 

The  specifications  only  allows  a  unit  shear  of  9000  Ibs.  per 
sq.  in.  (see  §41)  so  the  size  must  be  increased.  This  will  not 
change  the  shears  in  any  way,  but  will  change  the  required  bear- 
ing areas  and  lever  arms  and  moments. 

Required  area  for  shear=4Xl70000=25.2  sq  .in. 


A  5%  inch  pin  will  answer. 

In  a  similar  manner  the  pins  at  the  other  joints  are  figured 
with  the  following  results  : 

At  a  a  5%  inch  pin  is  required. 
At  c  a  5%  inch  pin  is  required. 
At  d  a  5%  inch  pin  is  required. 

It  will  make  the  shop  work  somewhat  less  if  these  pins  are 
all  made  the  same  size,  so  we  will  use  5%  inch  pins  at  a,  c,  d 
and  B. 


182 


RIVETED  TENSION  MEMBER. 


Art.  75. 


No  pin  is  used  at  &,  but  the  bottom  chord  is  run  through 
continuous  from  a  to  c,  and  a  riveted  connection  is  made  at  6 
between  Bb  and  the  chord  abc. 

'At  G  a  4%  inch  pin  is  required,  and  we  will  use  the  same 
size  at  D. 

Figures  68  to  71,  inclusive,  show  the  packing  at  the  various 
joints. 


Fig.  68. 
Packing  at  a. 


(      ^ 


Fig.  69. 
Packing  at  c. 


Fig.  70. 
Packing  at  d. 


Fig.  71. 
Packing  at 


75.  Details  of  a  Riveted  Tension  Member.  (11)  A  detail 
drawing  of  one  end  of  the  lower  chord  abc  is  shown  in  Fig.  72. 
The  width  of  the  member  is  determined  by  the  packing  at  a  <and  c 
as  shown  in  Figs.  68  and  69. 


Art.  75. 


RIVETED  TENSION  MEMBER. 


183 


The  maximum  stress  in  the  member  is  345,900  Ibs.  (DL-\-LL 
-f-Wind).  The  average  allowed  unit  stress  in  tension  is  15,520 
Ibs.  per  sq.  in.,  and  the  required  net  area  of  the  body  of  th£ 
member  is  22.29  sq.  in.  (See  Art.  64.)  According  to  the  speci- 
fications §68  the  net  section  through  the  pin  hole  must  be  one- 
third  in  excess  of  this  amount,  or  29.72  sq.  in.,  and  the  least 
section  back  of  the  pin  hole  60%  of  this,  or  17.83  sq.  in. 

The  net  section  of  the  2— 14"X%"  plates  through  the  pin 
hole  is 

2(2X21/8+2 1/(2i/2)2_|_(47/8)2_53/4_2)3/8==5.60  sq.  in. 

The  balance=29.72— 5.60=24.12  sq.  in.,  must  be  made  up 
of  pin  plates. 

The  effective  net  width  through  the  pin  hole  of  plates  16 
inches  wide  is  (See  Fig.  72) 


Fig.  72. 


(2X3y8+21/(2i/2)2+(47/8)2__53/4_2)=9.46  in. 
Then  the  required  thickness  for  pin  plates  16  inches  wide 
to  take  the  tension  is 
24.12 


9.46 


-=2.55  in.,  or  say  2%  inches. 


This  will  require  two  pin  plates  on  each  side  16"x%". 
The  average  allowed  unit  stress  in  bearing  on  the  pin 


184  RIVETED  TENSION  MEMBER.  Art.  75. 

oK/i/in 
(DL+LL+W)=      g^4u6  Xl.3=19,400  Ibs.  per  sq.  in.  (From 

*+ 40678" 

Eq.  (21)  and  Spec.  §39),  and  the  allowed  bearing  pressure  per 
linear  inch  of  pin  is  53/4x19400=111,550  Ibs. 

None  of  the  bearing  plates  can  however  be  counted  on  to 
take  more  stress  in  bearing  than  they  transmit  past  the  pin  hole 
in  tension. 

The  stress  transmitted  by  the  2— 14"X%"  plates  past  the 

r    of\ 

pin  hole  will  be  proportion/al  to  the  areas,  'and  is — : —  X  345,900= 

66,200  Ibs. 

The  stress  transmitted  by  the  other  pin  plates  is  345,900— 
66,200=279,700  Ibs. 

Then  the  required  bearing  thickness  of  the  16  inch  pin 

plates=^!™?=2.5  inches,  therefore  the  2-16"X%"  plates  on 
111560 

each  side  are  sufficient. 

1 7  8R 

The  required  net  length  back  of  the  pin  hole= =5.5  in. 

8.25 

Allowing  one  rivet  hole  out  this  will  requrie  the  pin  plates  to 
extend  51/£+l+2%=9%  inches  beyond  the  pin  center. 

The  stresses  taken  by  the  component  parts  of  the  body  of 
the  member  will  be  in  proportion  to  their  gross  areas  because 
their  deformations  must  be  equal,  and  the  connection  must  dis- 
tribute this  stress  properly  to  the  component  parts. 

The  stress  taken  in  the  body  of  the  member  by  1— 14"  X%" 

plate=-^-X  345,900=63,700  Ibs. 
218. 50 

The  stress  transmitted  past  the  pin  hole  by  each  of  the 
16"X%"  pin  plates=4£X 279,700=69,980  Ibs.,  and  sufficient 
rivets  must  be  provided  to  transmit  this  stress  from  the  pin 
plates  to  the  body  of  the  member. 

The  six  countersunk  rivets  between  the  pin  and  the  end  of 
the  angles  may  be  considered  as  transmitting  stress  from  the 
outside  pin  plate  to  the  14"  X%"  plate  so  long  -as  this  does  not 
raise  the  total  stress  in  that  plate  beyond  63,700  Ibs. 

The  value  of  the  six  countersunk  rivets  in  the  %  inch  plate 
is  6Xf  X4,922=12,660  Ibs.  (Spec.,  §40.)  This  would  bring 
the  total  stress  in  the  14"  X%"  plate  at  the  end  of  the  angles 


Art.  76.  TOP  CHORD  AND  END  POSTS.  186 

up  to  12,660+%  (66200)  =45,760  Ibs.,  which  is  less  than  63,700 
Ibs.,  and  therefore  safe. 

Further  rivets  will  be  required  in  the  outside  pin  plate  to 
transmit  69,980—12,660=57,320  Ibs.  The  rivets  will  be  in  single 

c  fro  OA 

shear  and  the  number  required^  -  =11. 

6412 

The  rivets  to  transmit  the  stress  from  the  inside  16"X%" 
pin  plate  must  be  placed  beyond  those  required  for  the  outside 

pin  plate.     The  number  required=-?-^-=13. 

5412 

The  required  net  area  of  the  body  of  the  member  through 
the  first  line  of  rivets  of  the  connection  plates  is  22.29  sq.  in., 
and  the  required  net  area  on  a  zig  zag  line  of  holes=1.3X  22.29 
=28.98  sq.  in.  (Spec.  §64.) 

Assuming  that  a  lacing  rivet  comes  opposite  the  first  rivet 
in  the  pin  plate  (which  is  not  exactly  the  case  here)  we  may 
write  an  equation  as  follows,  <and  solve  for  the  least  allowable 
pitch  of  rivets  in  the  connection  platte  <at  this  point.  (11). 
Calling  this  distance  x  we  have 


+2X% 
Solving  we  get  x=3y2  inches. 

This  pitch  may  safely  be  reduced  to  3  inches  after  the  first 
line  of  rivets  is  passed,  as  the  stress  in  the  body  of  the  member 
has  been  reduced  by  the  value  of  the  rivets  passed. 

The  lacing  of  a  tension  member  does  not  have  to  comply 
with  §97  of  the  specifications,  and  may  be  put  in  according  to 
the  judgment  of  the  engineer. 

76.  Location  of  Pins  in  Top  Chord  and  End  Posts.  (58). 
The  location  of  the  pins  in  the  top  chords  and  end  posts  depends 
upon  the  location  of  the  centers  of  gravity  of  the  sections  and 
upon  the  -amount  of  the  displacement  of  the  pins  necessary  to 
compensate  for  the  bending  due  to  the  weight  of  the  member. 

The  pin  at  the  hip  cannot  be  placed  in  the  exact  theoretical 
location  for  both  the  end  post  and  top  chord,  and  its  location 
must  necessarily  be  a  compromise  between  the  two. 


186 


TOP  CHORD  AND  END  POSTS. 


Art.  76. 


Fig.  73. 


Figure  73  shows  the  fac- 
tors which  must  be  taken  into 
consideration  in  this  problem. 
From  §43  of  the  specifications 
we  see  that  the  bending  mo- 
ment due  to  the  weight  of  the 
member  need  not  be  consid- 
ered unless  it  increases  the 
fiber  stress  more  than  10% 
above  the  allowed  unit. 
The  weight  of  the  end  posit  will  be  as  follows : 

1  Cover  plate      24"x%"    51.0 

2  Web  plates       21"x%"    89.2 
2  Side  plates       15"x%"    63.8 
2  Top         Ls  3"x3"x%"    23.0 
2  Bottom  Ls  4"x3"x%"    27.2 

254.2 

Details  say  10%=  25.8 

Total=280 . 0  Ibs.  per  lin.  ft. 

The  weight  per  linear  foot  horizontal  will  be  280  csc#=434 
Ibs.,  and  the  bending  moment  due  to  the  weight  will  be 


434X27* 
8 


The    maximum 
39550X12X9.48 


=39,550  ft.  Ibs. 
fiber    stress 


compressave    liber    stress    due    to    weight 
=  960  Ibs.  per  sq.  in.  in  the  top  of  the  cover 

rxww 

plate.  The  allowed  unit  stress  for  DL+LL  is  6516  Ibs.  per  sq. 
in.,  therefore  the  bending  moment  due  to  weight  must  be 
considered  in  the  end  post. 

The  maximum  compressive  fiber  stress  due  to  weight  or  to 
displacement  of  the  pins  may  reach  651  Ibs.  per  sq.  in. 

The  weight  of  the  end  section  of  the  top  chord  is  as  follows : 

1  Cover  plate      24"xi/2"    40.8 

2  Web  plates      18"xA"    68.8 
2  Top          Ls 3"x3"x3/8"    14.4 
2  Bottom    L54'/x3'/x^/     24.8 

148.8 
Details  say  10%=  14.2 

163.0  Ibs.  per  ft. 


Art.  77.  LACING.  ,  187 

The  bending  moment  due  to  the  weight  =168X272=14,880 

8 

ft.  Ibs.  The  distance  from  the  middle  of  the  web  to  the  center 
of  gravity  is  1.98  in.,  and  the  moment  of  inertia  about  the  hori- 
zontal axis  is  2230. 

The  maximum   compressive  fiber  stress  due  to  weight= 


-=612  n».  per  sq.  in. 


The  average  allowed  unit  stress  for  DL-\-LL  from  equation 
(21)  is  9490  Ibs.  per  sq.  in.,  therefore  the  bending  due  to  weight 
need  not  be  considered  in  the  top  chord. 

The  most  desirable  location  for  the  pin  will  be  obtained 
from  equation  (20)  as  follows: 


For  the  end  post  g  =1.00  in. 

10X378600 

For  the  top  chord  e=lg3X272><12=0.36  in. 
10X406800 

For  the  end  post  the  pin  should  be  1.77—1.00=0.77  in. 
above  the  center  line  of  the  web. 

For  the  top  chord  the  pin  should  be  1.98—0.36=1.62  in. 
above  the  center  line  of  the  web. 

If  x2  in  Fig.  73  is  made  8  in.  to  agree  with  the  most  desirable 
position  for  the  top  chord,  from  similar  triangles  x±  :  x2=d1  :  d2 
or  #1=9.33  in.,  which  would  place  the  pin  in  the  end  post  above 
the  center  of  gravity. 

If  XT_  is  made  lO1/?  in.  to  agree  with  the  most  desirable  posi- 
tion for  the  end  post,  #2=9.00  in. 

This  will  pla<ce  the  pin  %  in.  above  the  center,  of  the  web 
of  the  end  post  and  %  in.  above  the  <center  of  the  web  of  the  top 
chord.  This  location  will  be  used. 

The  pins  at  the  intermediate  top  chord  points  are  placed  on 
the  same  center  lines  at  those  at  the  hips,  as  they  only  have  to 
transmit  the  increments  of  stress  from  the  diagonals. 

Figure  74  is  a  detail  of  the  hip  joint. 

77.  Lacing  of  Compression  Members.  (58).  For  the  top 
chord  CD-  (which  is  the  largest)  the  allowed  unit  stress  for 

L 

20000—90  -  r 

DL  -|-  LL  from  equation  (21)  is    _  —=11  940—53  7  _  •= 

1.676  r 

9,920  Ibs.  per  sq.  in.   (using  the  radius  of  gyration  about  the 
vertical  axis.) 


188. 


LACING. 


Art.  77. 


74. 


From  equation  (18) 


s.  per  inch. 

Length  of  member  covered  by  one  lace  bar  (single  lacing, 
Spec.  §97)=22i/4  cot.  60°=12.8  in. 

Longitudinal  increment  of  stress  taken  by  one  bar=497X 
12.8X%=3180  Ibs.  (Half  is  taken  by  cover  plate.) 


Art.  77.  LAOING.  189 

Stress  in  one  bar=3180  sec.  60°=6360  Ibs. 
In  the  lattice  it  is  safe  to  use  the  unit  stresses  allowed  for 
lateral  bracing. 

Specifications  §97  requires  the  lattice  for  this  chord  to  be 
%  in.  thick. 

Allowed  unit  stress  in  compression  is 

13000-60  IL  =13000—  60X256=4520  Ibs.  per  sq.  in. 


6360 

=1.41  sq.  in. 
4520 

Required  width=  *'41  —2.26  in, 
,625 

Use  lace  bars  3"x%"  for  top  chords  to  comply  with  speci- 
fications §97. 

The  lacing  for  the  end  posts  cannot  be  obtained  directly 
from  equation  (18)  because  1Jhe  end  post  carries  transverse  shear 
in  addition  to  the  direct  stress. 

The  total  difference  in  extreme  fiber  stress  due  to  column 
action  is  obtained  from  the  column  formula  for  DL-\-LL+  Wind. 
From  Eq.  (21) 

L 

17000—90  —  •  L 

Sc==.  -    I6?5r    Xl.3=13,200-69.8  — 

The  values  of  L  and  r  here  must  be  taken  about  a  vertical 
axis  because  we  are  figuring  for  the  shear  in  that  direction. 

The  difference  in  unit  stresses  due  to  column  action=69.8X 

?i>|-2  =3280  Ibs.  per  sq.  in. 

The  difference  in  unit  stresses  due  to  transverse  bending 
from  Art.  66  ==  3310  Ibs.  per  sq.  in. 

Total  difference=3310+3280=6590  Ibs.  per  sq.  in. 

Total  stress  to  be  transferred  by  the  lacing  and  cover  plate 
in  a  distance  of  17  ft.  (distance  from  end  to  point  of  contra- 
flexure)=6590X^-i=6590X35.1=231,300  Ibs. 


f=  =1134  Ibs.  per  inch. 

17X12 

Longitudinal  increment  of  stress  taken  by  one  bar=1134X 
12.8X%=7260  Ibs. 

Total  stress  in  one  bar=7260  sec.  60°=14,520  Ibs. 


190  LACING.  Art.  77. 

Using  bars  %  in.  thick,  the  allowed  compressive  unit  stress 
is  4520  Ibs.  per  sq.  in. 

Required  area^-^>.=3.21  sq.  in. 

Required  width=-^~  =5.12  in. 

Use  lace  bars  5"x%"  with  two  rivets  in  each  end. 

For  the  intermediate  posts  Cc,  the  radius  of  gyration  per- 
pendicular to  the  channel  webs  is  4.31  in,,  and  the  unsupported 
length  in  that  direction  about  21  ft. 

The  allowed  unit  stress  for  Z>L+LL=10,060— 53.25  — 

(See  Art.  65)  =6950  Ibs.  per  sq.  in. 

From  equation  (18)  we  get 

4X11.76X8110^0  lbg>  inch 

21X12 

The  length  covered  by  one  lace  bar  (single  lacing,  Spec.  §97) 
is  3%  inches. 

Longitudinal  increment  of  stress  taken  by  one  bar=580X 
3%X1/2=31015  Ibs.     (Lacing  on  two  sides.) 
Stress  in  one  bar=1015  sec.  ,60°=2030  Ibs. 
'Specifications  §97  requires  that  the  lacing  for  this  case 
inches  thick,  but  §82  limits  us  to  %  in. 


Allowed  unit  stress=13000— ^^=9100  Ibs.  per  sq.  in. 

.  108 

Required  area=-?222-  =0.23  sq.  in. 
yioo 

Required  width=-^— =0.61  in. 
.375 

Specifications  §97  requires  2y2  in.  X  %  in. 

For  post  Dd  specifications  requires  lacing  2i/4"x%". 

78.  Details  of  the  Floor  Beams.  Figure  75  shows  a  detail 
drawing  of  one  of  the  intermediate  floor  beams.  Cooper's  speci- 
fications requires  the  use  of  a  number  of  different  unit  stresses 
for  rivets  in  various  positions,  (and  these  must  be  kept  in  mind. 
X§40) 

QOfiOO 

Rivets  required  for  stringer  connection=  —-—==35. 

2625 


Art.  78.  FLOOR  BEAMS.  191 

Rivets   required  for   end   connection   angles   through  web 
«00 
8659 


90800       .. 
=11. 


QOftftO 

Eivets  required  for  end  connection  to  post= =32. 

86100 

Rivets  required  for  connection  of  flanges  to  web= =23. 

3938 

(Shop  rivets  in  bearing  on  %  in.  web.) 

At  the  end  of  the  bottom  flange  the  expedient  is  resorted 
to  of  riveting  a  plate  on  top  of  the  angles  to  transfer  a  part  of 
the  stress  to  the  web.  This  then  gives  us  the  following  value : 

16  rivets  bearing  on  %  in.  web=16X3938=  63,000  Ibs. 
6  rivets  double  shear  =$  6X8659=  51,900  Ibs. 

114,900  Ibs. 
The  top  flange  has  26  rivets  effective. 

Rivets  required  for  web  splice= =23. 


oooo  o;    9   o    o    o  ( 


INDEX 


Art.  Page 

Adding  machines 18  37 

Angles — maximum   lengths    52  124 

Bearing  plates  for  plate  girder 82  132 

Bending  of  chords  due  to  weight  58  145 

Bolsters  for  plate  girder  52  132 

Books  of  reference  25  50 

Bottom,  lateral  bracing  70  170 

Box  girders  42  99 

Building  construction  37  80 

Built  tension  memlbers   ©7  141 

tension  members   64  162 

Butt  joints 8  12 

Button  head  rivets  1  1 

Calculation  of  pins  74  178 

Center  of  gravity 65  157 

Chcxrds — Design  of   65  156 

— Location  of  pins 76  185 

Classes  of  structural  steel  work 14  29 

Clearances    27  60 

Columns    58  142 

Compression  and  bending  combined 58  144 

Compression  members    58  142 

—Allowance  for  rivet  holes ...  4  5 

—Design  of    65  154 

—Width  of  66  155 

Contracts  and  proposals  16  30 

Corrugated  iron  or  steel  36  77 

Countersunk  rivets  1  1 

Countersunk  rivet  values  9  15 

Dead  load    , 61  147 

for  plate  girder  bridge 6i2  116 

of  truss  bridges  56  141 

Dead  loads— Roof    40  86 

Deck  plate  girder  bridge  design   52  115 

estimate  52  134 

stress  sheet  52  136 

Depth  of  truss    > 62  147 

Depth  of  trusses    &5  139 

108 


194  INDEX. 

Art.  Page 

Design  of  chords 65  156 

compression  members  6S  154 

end  posts  66  159 

deck  plate  girder  bridge 5)2  115 

floor  beam 68  165 

pin-connected  bridge   60  146 

Pprtal   67  163 

riveted  connections 9  13 

a  roof   40  84 

a  stringer  51  110 

tension  members  64  150 

Designing  and  estimating 17  31 

Designing  and  estimating Chap.  II  29 

Details — Duplication  of  27  '58 

floor  beams  78  190 

hip  joint  76  188 

pin  connected  bridges  Chap.  VII  177 

a  riveted  tension  member 75  182 

Dolly   3  4 

Drafting  department    i 24  46 

Draftsman's  equipment 25  47 

Drawing  boards    24  47 

instruments    25  48 

pencils    25  49 

room  light   24  47 

table    24  47 

Drawings  for  roof  trusses  41  92 

Drawing  of  roof  truss  . .  98 

Drift  pins 2  3 

Driving  rivets  3  3 

Eccentricity  of  pins  in  dhord  members 58  145 

Economic  depth  of  girders  46  103 

girders   51  111 

girders   52  119 

trusses   55  139 

Effective  depth  of  plate  girders 415  103 

End  floor  beam   68  167 

End  posts — Design  of 06  159 

—Lacing 77  189 

Equivalent  loads   66  140 

Erection    23  45 

Erection  and  manufacture  Chap.  Ill  44 

Estimate  for  deck  plate  girder  'bridge  52  134 

for  pin  connected  bridge  72  173 

of  weight  of  stringers 51  115 

Estimates  of  cost 17  31 

Estimates— Forms  of  17  33 


INDEX.  195 

Art.  Page 

Estimating  and  designing 17  31 

and  designing Chap.  II  29 

— Order  of    19  37 

— Order  for  highway  bridges   19  39 

— Order  for  railway  bridges  19  38 

• — Order  for  steel   buildings    19  40 

Eye  bars  57  141 

False  work 23  45 

Field  riveting    23  46 

Field  rivet  values   9  14 

Flange  plates  of  plate  girders 52  121 

riveting  in  plane  girders 4*9  107 

riveting  in  plate  igirders ol  113 

iriveting  in  plate  girders 52  122 

sections  42  99 

splices  in  plate  girders  5*0  110 

splices  in  plate  girders  52  124 

Flanges  of  girders 45  102 

girders  51  112 

girders  52  120 

Floor  beams — 'Details    78  190 

—Details    78  192 

—Design 68  165 

Floor — Design  of,  for  (bridge  52  115 

Freight    31  69 

Gallows  frame    23  45 

General  plans 21  42 

Girders Chap.  V  99 

— Economic  depth  46  103 

—Effective  depth    45  103 

— The  flanges   45  102 

— -Flange  riveting    48  107 

• — Flange  splices 50  110 

— 'Maximum  lengths   42  99 

^-Moment  of  resistance 43  99 

—Shear  distribution  44  100 

— Stiffeners    47  105 

— Stresses   43  99 

— Stresses    51  112 

— Stresses   52  117 

—The  web  44  100 

—Web   splices    48  106 

Grip  of  rivets  1  1 

Heating  rivets 3  4 

Hip  joint— Detail  of  76  188 

pin 74  178 

Inertia — Moment  of   .                             65  158 


196  INDEX. 

Art.  Page 

Inspection    : 33  75 

Intermediate  posts — Lacing  71?  190 

Jack  rafters 37  80 

Joints— Butt   8  12 

—Lap    8  12 

Lacing  of  compression  members  68  143 

compression  members  ' 77  187 

Lap  joints    8  12 

Laterals—Bottom    70  170 

Lateral  bracing  df  plate  girders   62  12(7 

stringers    61  114 

Lateral  systems   59  146 

Laterals — Top  69  169 

Loads 66  140 

Loads*— {Roof    38  81 

Location  of  pins  in  top  chord  and  end  posts 76  1<85 

Manufacture  and  erection Chap.  HI  44 

Materials  32  70 

Material  orders  26  51 

Moment  in  deck  plate  girder  5'2  117 

Moment  of  inertia  65  158 

Moment  of  resistance  of  plate  girder 43  100 

Net  sections  of  tension  members 11  20 

Order  of  estimating    19  37 

highway  bridges   19  39 

railway  bridges   19  38 

steel  buildings   19  40 

Order  of  procedure  for  a  -pin  connected  (bridge 28  62 

for  plate  girder  bridge 2'9  65 

Ordering  material  '26  51 

Packing  73  178 

Packing  at  various  joints  74  182 

Panel   lengths    55  139 

Pins    73  177 

Pins^-Caloulation    74  178 

Pin-connected  bridges    Chap.  VI  139 

—Design   of    60  146 

details   <Chap.  VII  177 

— ^Estimate 72  173 

— Order  of  procedure  for 28  62 

stresses    63  148 

-iStress  sheet   7'2  176 

Pins— (Location  in  top  chord  and  end  posts 76  185 

Pin  plates    10  16 

Pin  plates    10  18 

Pitch  of  rivets  defined    7  10 

Pitch  of  roofs    ,  36  78 


INDEX.  197 

Art.  Page 

Plans— General    21  42 

Plans— Show    21  43 

Plate  girder  bridges    Chap.  V  99 

Plate  girder  bridge — Order  of  procedure  29  65 

Plato  girder  design    62  115 

Plate  girders— 'Economic  depth   46  103 

— Economic  depth   51  111 

— Economic  depth   52  119 

—Effective   depth    45  103 

—Effective   depth    51  112 

—Effective    de,pth    52  120 

—Flanges    45  102 

—Flanges    51  112 

—Flanges    '52  120 

—Flange  plates    52  121 

—Flange  riveting    49  107 

— Flange  riveting    51  113 

— Flange  riveting    62  122 

—Flange  splices    50  ll'i) 

• — Flange  splices    52  124 

— Lateral   bracing    52  127 

' — Maximum   moment    52  117 

— Stiffeners    47  105 

— Stiffeners    51  114 

-nStiffeners '52  124 

—Stresses    43  99 

— Stresses    51  112 

^Stresses    52  117 

—Web    -. 44  100 

—Web    51  111 

—Web     52  120 

—Web  splices    48  106 

—Web  splices    52  120 

Plates— Sizes  of  26  53 

Pony  trusses 55  140 

Portal  bracing   67  163 

Proposals  and  contracts  16  30 

Purlins    40  86 

Radius  of  gyration   66  15i7 

Rafter  design,  for  a  roof  truss  40  88 

Reaming    2  2 

Rivet  holes    2  2 

— Allowance  for  in  compression  members  4  5 

in  tension  members   11  20 

Rivet  pitch  in  flanges  of  girders 49  107 

Rivet  spacing    27  59 

Riveted  joints — Alternating  stresses   4  7 


198  INDEX. 

Art.  Page 

Riveted  joints — Alternating  stresses    &  9 

— Assumption  made  in  design  of 4  5 

—Design  of    9  13 

—Examples    10  15 

—Friction  in    4  6 

— 7Kind>s  of   8  12 

— Manner  of  failure    9  13 

— Requirements  for  good    5  9 

—Slip  in 4  6 

Riveted  tension  member  details   75>  182 

Riveted  truss  bridges    -. 28  64 

Riveting    Ohap.  I  1 

—•Chain    9  13 

— Design  of  joints  in  a  roof  truss 41  95 

of  flanges  of  plate  girders 49  107 

of  flanges  of  plate  girders 51  113 

of  flanges  of  plate  girders 52  122 

machines   3  3 

of  pin  plates   10'  16 

of  pin  plates  10  18 

-Staggered    9  13 

—Theory  of   4i  4 

Rivets — American  Bridge  Company's  standard 1  1 

— ^Bending  in  4  7 

— 'Button  heads    1  1 

'-Conventional  signs  for   13  28 

— Countersunk    1  1 

-^Dimensions  of 1  1 

— 'Driving    3  3 

— Field  values    9  14 

— Orip    1  1 

—Heating    3  4 

— Initial  tension  in  4  6 

— Length  required    1  2 

t— Shape  of  heads   1  1 

—Proper  size®  ,  6  9 

>— Spacing  of  7  10 

. — Values  of  countersunk 9  15 

— Working  stresses   9  14 

Roller®   71  171 

Roofs   Chap.  IV  77 

construction    34  77 

coverings    35  77 

—Dead  load   40  86 

—Design  of  a  40  84 

loads    38  81 

pitch  for  various  coverings 35  78 


INDEX.  199 

Art.  Page 

Roof  purlins    40  86 

truss  drawings    41  92 

truss  drawing   41  94 

trusses — Types  of  3(6  78 

Scales    26  49 

for  roof  truss  drawing 41  94 

/for  shop  drawing 28  63 

Shear— 'Distribution  over  -cross  section  of  girder 44  100 

Shear  in  girders   44  100 

•Shear  in  girders  51  111 

Shear  in  girders   &2  118 

Shipment    31  69 

Shoes  for  plate  girder  52  132 

Shoes  and  rollers   71  171 

Shop  bills    30  67 

Shop  drawings    27  54 

drawings-- Methods  of  working  up  i21T  61 

drawings — Notes  on   27  68 

drawings  for  roof  truss  41  92 

drawings  for  roof  truss  41  96 

drawings — Titles  on   27  56 

Shop  operations    22  44 

Shops — Kinds  of   15  30 

Show  plans   21  43 

Signs  for  rivets  on  drawings W  28 

Sizes  of  rivets  1  1 

Sizes  of  rivets   6  9 

Slide  rules    18  35 

—Duplex    18  36 

— Engineer's    18  36 

—Fuller's    18  35 

— Manheim    18  35 

—Rule  for  operation  of 18  36 

—Thacher's    16  35 

«— J Three  multiple   18  36 

Snap  for  rivet  heads  3  4 

Snow  loads   38  83 

Solid  floors    53  138 

Spacing  of  rivets  7  10 

Specifications    20  41 

Bplices  in  flanges  of  plate  girders 52  124 

— Flanges  of  girders 50  110 

in  webs  of  plate  girders 48  106 

in  webs  of  plate  girders 52  125 

Bteel— Acid    32  72 

—Baste    32  72 

— Bessemer    .                   32  71 


200  INDEX. 

Art.  Page 

Steel— Effect  of  cartoon  32  71 

—Open  hearth    32  72 

— Physical  characteristics    32  70 

— Process  of  manufacture  32  71 

— "Specifications  for  32  70 

—Tests  of   32  74 

Stiffened    29  65 

Stiffeners    : 47  105 

Stiffeners 5i  114 

Stiffeners 62  124 

Stiffeners— Crimped    4tf  105 

Stress  sheets    21  42 

for  deck  plate  girder  bridge 52  136 

•for  pin  connected  bridge  72  176 

for  a  roof  40  90 

Stresses  in  girders    43  99 

in  girders    : 51  112 

in  girders    52  117 

in  pin  connected  bridge   63  148 

in  roof  trusses   39  84 

in  roof  trusses   40  87 

in  trusses  of  bridge  due  to  wind 63  149 

Stringer — Design    51  110 

—Estimate  of  weight  51  115 

laterals   51  114 

Structural  steel— Classes  of   14  29 

Templets 22  44 

Tension  memlbers 57  141 

— ®uilt    64  152 

—Details  of  riveted   75  182 

— Design  of  64  150 

—Net  sections   11  20 

Tension  on  rivet  heads  4>  6 

Tests  of  steel  32  74 

Theory  of  riveting  4  4 

Through  plate  girders  63  137 

Ties— Design  of  for  bridge  52  115 

Time  savers    18  3<5 

Titles  on  shop  drawings  27  56 

Top  chord— Lacing    77  187 

Top  lateral  bracing   69  169 

Tracing  linen   27  54 

Traveler    45 

Trusses — Types  of    35  139 

Types  of  plate  girder  flanges  42  99 

Types  of  roof  trusses   36  78 

Types  of  trusses 55  139 


INDEX.  201 

Art.  Page 

Webs  of  Girders. 44  100 

of  girders 51  111 

of  girders  52  120 

— Moment  of  resistance   44  101 

— Moment  of  resistance  45  102 

splices  in  plate  girders 48  106 

splices  in  plate  girders  52  125 

Width  of  compression  members  65  155 

Wind  pressure   38  82 


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